Symmetrization And Stabilization Of Solutions Of Nonlinear Elliptic Equations

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Symmetrization and Stabilization of Solutions of Nonlinear Elliptic Equations

Author : Messoud Efendiev
Publisher : Springer
ISBN 13 : 3319984071
Total Pages : 273 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Symmetrization and Stabilization of Solutions of Nonlinear Elliptic Equations by : Messoud Efendiev

Download or read book Symmetrization and Stabilization of Solutions of Nonlinear Elliptic Equations written by Messoud Efendiev and published by Springer. This book was released on 2018-10-17 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with a systematic study of a dynamical system approach to investigate the symmetrization and stabilization properties of nonnegative solutions of nonlinear elliptic problems in asymptotically symmetric unbounded domains. The usage of infinite dimensional dynamical systems methods for elliptic problems in unbounded domains as well as finite dimensional reduction of their dynamics requires new ideas and tools. To this end, both a trajectory dynamical systems approach and new Liouville type results for the solutions of some class of elliptic equations are used. The work also uses symmetry and monotonicity results for nonnegative solutions in order to characterize an asymptotic profile of solutions and compares a pure elliptic partial differential equations approach and a dynamical systems approach. The new results obtained will be particularly useful for mathematical biologists.

Singular Solutions of Nonlinear Elliptic and Parabolic Equations

Author : Alexander A. Kovalevsky
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110390086
Total Pages : 531 pages
Book Rating : 4.1/5 (13 download)

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Book Synopsis Singular Solutions of Nonlinear Elliptic and Parabolic Equations by : Alexander A. Kovalevsky

Download or read book Singular Solutions of Nonlinear Elliptic and Parabolic Equations written by Alexander A. Kovalevsky and published by Walter de Gruyter GmbH & Co KG. This book was released on 2016-03-21 with total page 531 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph looks at several trends in the investigation of singular solutions of nonlinear elliptic and parabolic equations. It discusses results on the existence and properties of weak and entropy solutions for elliptic second-order equations and some classes of fourth-order equations with L1-data and questions on the removability of singularities of solutions to elliptic and parabolic second-order equations in divergence form. It looks at localized and nonlocalized singularly peaking boundary regimes for different classes of quasilinear parabolic second- and high-order equations in divergence form. The book will be useful for researchers and post-graduate students that specialize in the field of the theory of partial differential equations and nonlinear analysis. Contents: Foreword Part I: Nonlinear elliptic equations with L^1-data Nonlinear elliptic equations of the second order with L^1-data Nonlinear equations of the fourth order with strengthened coercivity and L^1-data Part II: Removability of singularities of the solutions of quasilinear elliptic and parabolic equations of the second order Removability of singularities of the solutions of quasilinear elliptic equations Removability of singularities of the solutions of quasilinear parabolic equations Quasilinear elliptic equations with coefficients from the Kato class Part III: Boundary regimes with peaking for quasilinear parabolic equations Energy methods for the investigation of localized regimes with peaking for parabolic second-order equations Method of functional inequalities in peaking regimes for parabolic equations of higher orders Nonlocalized regimes with singular peaking Appendix: Formulations and proofs of the auxiliary results Bibliography

Compactness and Stability for Nonlinear Elliptic Equations

Author : Emmanuel Hebey
Publisher : Erich Schmidt Verlag GmbH & Co. KG
ISBN 13 : 9783037191347
Total Pages : 308 pages
Book Rating : 4.1/5 (913 download)

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Book Synopsis Compactness and Stability for Nonlinear Elliptic Equations by : Emmanuel Hebey

Download or read book Compactness and Stability for Nonlinear Elliptic Equations written by Emmanuel Hebey and published by Erich Schmidt Verlag GmbH & Co. KG. This book was released on 2014 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book offers an expanded version of lectures given at ETH Zurich in the framework of a Nachdiplomvorlesung. Compactness and stability for nonlinear elliptic equations in the inhomogeneous context of closed Riemannian manifolds are investigated. This field is presently undergoing great development. The author describes blow-up phenomena and presents the progress made over the past years on the subject, giving an up-to-date description of the new ideas, concepts, methods, and theories in the field. Special attention is devoted to the nonlinear stationary Schrodinger equation and to its critical formulation. Intended to be as self-contained as possible, the book is accessible to a broad audience of readers, including graduate students and researchers.

Qualitative Analysis of Nonlinear Elliptic Partial Differential Equations

Author : Vicentiu D. Radulescu
Publisher : Hindawi Publishing Corporation
ISBN 13 : 9774540395
Total Pages : 205 pages
Book Rating : 4.7/5 (745 download)

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Book Synopsis Qualitative Analysis of Nonlinear Elliptic Partial Differential Equations by : Vicentiu D. Radulescu

Download or read book Qualitative Analysis of Nonlinear Elliptic Partial Differential Equations written by Vicentiu D. Radulescu and published by Hindawi Publishing Corporation. This book was released on 2008 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive introduction to the mathematical theory of nonlinear problems described by elliptic partial differential equations. These equations can be seen as nonlinear versions of the classical Laplace equation, and they appear as mathematical models in different branches of physics, chemistry, biology, genetics, and engineering and are also relevant in differential geometry and relativistic physics. Much of the modern theory of such equations is based on the calculus of variations and functional analysis. Concentrating on single-valued or multivalued elliptic equations with nonlinearities of various types, the aim of this volume is to obtain sharp existence or nonexistence results, as well as decay rates for general classes of solutions. Many technically relevant questions are presented and analyzed in detail. A systematic picture of the most relevant phenomena is obtained for the equations under study, including bifurcation, stability, asymptotic analysis, and optimal regularity of solutions. The method of presentation should appeal to readers with different backgrounds in functional analysis and nonlinear partial differential equations. All chapters include detailed heuristic arguments providing thorough motivation of the study developed later on in the text, in relationship with concrete processes arising in applied sciences. A systematic description of the most relevant singular phenomena described in this volume includes existence (or nonexistence) of solutions, unicity or multiplicity properties, bifurcation and asymptotic analysis, and optimal regularity. The book includes an extensive bibliography and a rich index, thus allowing for quick orientation among the vast collection of literature on the mathematical theory of nonlinear phenomena described by elliptic partial differential equations.

Fully Nonlinear Elliptic Equations

Author : Luis A. Caffarelli
Publisher : American Mathematical Soc.
ISBN 13 : 0821804375
Total Pages : 114 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Fully Nonlinear Elliptic Equations by : Luis A. Caffarelli

Download or read book Fully Nonlinear Elliptic Equations written by Luis A. Caffarelli and published by American Mathematical Soc.. This book was released on 1995 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of the book is to extend classical regularity theorems for solutions of linear elliptic partial differential equations to the context of fully nonlinear elliptic equations. This class of equations often arises in control theory, optimization, and other applications. The authors give a detailed presentation of all the necessary techniques. Instead of treating these techniques in their greatest generality, they outline the key ideas and prove the results needed for developing the subsequent theory. Topics discussed in the book include the theory of viscosity solutions for nonlinear equations, the Alexandroff estimate and Krylov-Safonov Harnack-type inequality for viscosity solutions, uniqueness theory for viscosity solutions, Evans and Krylov regularity theory for convex fully nonlinear equations, and regularity theory for fully nonlinear equations with variable coefficients.

Linear and Nonlinear Non-Fredholm Operators

Author : Messoud Efendiev
Publisher : Springer Nature
ISBN 13 : 9811998809
Total Pages : 217 pages
Book Rating : 4.8/5 (119 download)

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Book Synopsis Linear and Nonlinear Non-Fredholm Operators by : Messoud Efendiev

Download or read book Linear and Nonlinear Non-Fredholm Operators written by Messoud Efendiev and published by Springer Nature. This book was released on 2023-02-04 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to a new aspect of linear and nonlinear non-Fredholm operators and its applications. The domain of applications of theory developed here is potentially much wider than that presented in the book. Therefore, a goal of this book is to invite readers to make contributions to this fascinating area of mathematics. First, it is worth noting that linear Fredholm operators, one of the most important classes of linear maps in mathematics, were introduced around 1900 in the study of integral operators. These linear Fredholm operators between Banach spaces share, in some sense, many properties with linear maps between finite dimensional spaces. Since the end of the previous century there has been renewed interest in linear – nonlinear Fredholm maps from a topological degree point of view and its applications, following a period of “stagnation" in the mid-1960s. Now, linear and nonlinear Fredholm operator theory and the solvability of corresponding equations both from the analytical and topological points of view are quite well understood. Also noteworthy is, that as a by-product of our results, we have obtained an important tool for modelers working in mathematical biology and mathematical medicine, namely, the necessary conditions for preserving positive cones for systems of equations without Fredholm property containing local – nonlocal diffusion as well as terms for transport and nonlinear interactions.

A Symmetrization Result for Nonlinear Elliptic Equations

Author : Vincenzo Ferone
Publisher :
ISBN 13 :
Total Pages : 18 pages
Book Rating : 4.:/5 (897 download)

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Book Synopsis A Symmetrization Result for Nonlinear Elliptic Equations by : Vincenzo Ferone

Download or read book A Symmetrization Result for Nonlinear Elliptic Equations written by Vincenzo Ferone and published by . This book was released on 2002 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Nonlinear Elliptic Equations and Nonassociative Algebras

Author : Nikolai Nadirashvili
Publisher : American Mathematical Soc.
ISBN 13 : 1470417103
Total Pages : 250 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Nonlinear Elliptic Equations and Nonassociative Algebras by : Nikolai Nadirashvili

Download or read book Nonlinear Elliptic Equations and Nonassociative Algebras written by Nikolai Nadirashvili and published by American Mathematical Soc.. This book was released on 2014-12-03 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents applications of noncommutative and nonassociative algebras to constructing unusual (nonclassical and singular) solutions to fully nonlinear elliptic partial differential equations of second order. The methods described in the book are used to solve a longstanding problem of the existence of truly weak, nonsmooth viscosity solutions. Moreover, the authors provide an almost complete description of homogeneous solutions to fully nonlinear elliptic equations. It is shown that even in the very restricted setting of "Hessian equations", depending only on the eigenvalues of the Hessian, these equations admit homogeneous solutions of all orders compatible with known regularity for viscosity solutions provided the space dimension is five or larger. To the contrary, in dimension four or less the situation is completely different, and our results suggest strongly that there are no nonclassical homogeneous solutions at all in dimensions three and four. Thus this book gives a complete list of dimensions where nonclassical homogeneous solutions to fully nonlinear uniformly elliptic equations do exist; this should be compared with the situation of, say, ten years ago when the very existence of nonclassical viscosity solutions was not known.

Numerical Solution of Nonlinear Elliptic Problems Via Preconditioning Operators

Author : István Faragó
Publisher : Nova Publishers
ISBN 13 : 9781590333761
Total Pages : 424 pages
Book Rating : 4.3/5 (337 download)

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Book Synopsis Numerical Solution of Nonlinear Elliptic Problems Via Preconditioning Operators by : István Faragó

Download or read book Numerical Solution of Nonlinear Elliptic Problems Via Preconditioning Operators written by István Faragó and published by Nova Publishers. This book was released on 2002 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Solution of Nonlinear Elliptic Problems Via Preconditioning Operators - Theory & Applications

Morse Index of Solutions of Nonlinear Elliptic Equations

Author : Lucio Damascelli
Publisher : de Gruyter
ISBN 13 : 9783110537321
Total Pages : 0 pages
Book Rating : 4.5/5 (373 download)

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Book Synopsis Morse Index of Solutions of Nonlinear Elliptic Equations by : Lucio Damascelli

Download or read book Morse Index of Solutions of Nonlinear Elliptic Equations written by Lucio Damascelli and published by de Gruyter. This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is devoted to the publication of high-level monographs which cover the whole spectrum of current nonlinear analysis and applications in various fields, such as optimization, control theory, systems theory, mechanics, engineering, and other sciences. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of nonlinear analysis. Contributions which are on the borderline of nonlinear analysis and related fields and which stimulate further research at the crossroads of these areas are particularly welcome. Editor-in-Chief J rgen Appell, W rzburg, Germany Honorary and Advisory Editors Catherine Bandle, Basel, Switzerland Alain Bensoussan, Richardson, Texas, USA Avner Friedman, Columbus, Ohio, USA Umberto Mosco, Worcester, Massachusetts, USA Louis Nirenberg, New York, USA Alfonso Vignoli, Rome, Italy Editorial Board Manuel del Pino, Bath, UK, and Santiago, Chile Mikio Kato, Nagano, Japan Wojciech Kryszewski, Toruń, Poland Vicenţiu D. Rădulescu, Krak w, Poland Simeon Reich, Haifa, Israel Please submit book proposals to J rgen Appell. Titles in planning include Lucio Damascelli and Filomena Pacella, Morse Index of Solutions of Nonlinear Elliptic Equations (2019) Tomasz W. Dlotko and Yejuan Wang, Critical Parabolic-Type Problems (2019) Rafael Ortega, Periodic Differential Equations in the Plane: A Topological Perspective (2019) Ireneo Peral Alonso and Fernando Soria, Elliptic and Parabolic Equations Involving the Hardy-Leray Potential (2020) Cyril Tintarev, Profile Decompositions and Cocompactness: Functional-Analytic Theory of Concentration Compactness (2020) Takashi Suzuki, Semilinear Elliptic Equations: Classical and Modern Theories (2021)

Nonlinear Second Order Elliptic Equations

Author : Mingxin Wang
Publisher : Springer Nature
ISBN 13 : 9819986923
Total Pages : 319 pages
Book Rating : 4.8/5 (199 download)

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Book Synopsis Nonlinear Second Order Elliptic Equations by : Mingxin Wang

Download or read book Nonlinear Second Order Elliptic Equations written by Mingxin Wang and published by Springer Nature. This book was released on with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Sobolev and Viscosity Solutions for Fully Nonlinear Elliptic and Parabolic Equations

Author : N. V. Krylov
Publisher : American Mathematical Soc.
ISBN 13 : 1470447401
Total Pages : 458 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Sobolev and Viscosity Solutions for Fully Nonlinear Elliptic and Parabolic Equations by : N. V. Krylov

Download or read book Sobolev and Viscosity Solutions for Fully Nonlinear Elliptic and Parabolic Equations written by N. V. Krylov and published by American Mathematical Soc.. This book was released on 2018-09-07 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book concentrates on first boundary-value problems for fully nonlinear second-order uniformly elliptic and parabolic equations with discontinuous coefficients. We look for solutions in Sobolev classes, local or global, or for viscosity solutions. Most of the auxiliary results, such as Aleksandrov's elliptic and parabolic estimates, the Krylov–Safonov and the Evans–Krylov theorems, are taken from old sources, and the main results were obtained in the last few years. Presentation of these results is based on a generalization of the Fefferman–Stein theorem, on Fang-Hua Lin's like estimates, and on the so-called “ersatz” existence theorems, saying that one can slightly modify “any” equation and get a “cut-off” equation that has solutions with bounded derivatives. These theorems allow us to prove the solvability in Sobolev classes for equations that are quite far from the ones which are convex or concave with respect to the Hessians of the unknown functions. In studying viscosity solutions, these theorems also allow us to deal with classical approximating solutions, thus avoiding sometimes heavy constructions from the usual theory of viscosity solutions.

Contributions to Nonlinear Elliptic Equations and Systems

Author : Alexandre N. Carvalho
Publisher : Birkhäuser
ISBN 13 : 3319199021
Total Pages : 434 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Contributions to Nonlinear Elliptic Equations and Systems by : Alexandre N. Carvalho

Download or read book Contributions to Nonlinear Elliptic Equations and Systems written by Alexandre N. Carvalho and published by Birkhäuser. This book was released on 2015-11-14 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume of contributions pays tribute to the life and work of Djairo Guedes de Figueiredo on the occasion of his 80th birthday. The articles it contains were born out of the ICMC Summer Meeting on Differential Equations – 2014 Chapter, also dedicated to de Figueiredo and held at the Universidade de São Paulo at São Carlos, Brazil from February 3-7, 2014. The contributing authors represent a group of international experts in the field and discuss recent trends and new directions in nonlinear elliptic partial differential equations and systems. Djairo Guedes de Figueiredo has had a very active scientific career, publishing 29 monographs and over one hundred research articles. His influence on Brazilian mathematics has made him one of the pillars of the subject in that country. He had a major impact on the development of analysis, especially in its application to nonlinear elliptic partial differential equations and systems throughout the entire world. The articles collected here pay tribute to him and his legacy and are intended for graduate students and researchers in mathematics and related areas who are interested in nonlinear elliptic partial differential equations and systems.

Variational Methods for the Numerical Solution of Nonlinear Elliptic Problem

Author : Roland Glowinski
Publisher : SIAM
ISBN 13 : 1611973783
Total Pages : 473 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Variational Methods for the Numerical Solution of Nonlinear Elliptic Problem by : Roland Glowinski

Download or read book Variational Methods for the Numerical Solution of Nonlinear Elliptic Problem written by Roland Glowinski and published by SIAM. This book was released on 2015-11-04 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: Variational Methods for the Numerical Solution of Nonlinear Elliptic Problems?addresses computational methods that have proven efficient for the solution of a large variety of nonlinear elliptic problems. These methods can be applied to many problems in science and engineering, but this book focuses on their application to problems in continuum mechanics and physics. This book differs from others on the topic by presenting examples of the power and versatility of operator-splitting methods; providing a detailed introduction to alternating direction methods of multipliers and their applicability to the solution of nonlinear (possibly nonsmooth) problems from science and engineering; and showing that nonlinear least-squares methods, combined with operator-splitting and conjugate gradient algorithms, provide efficient tools for the solution of highly nonlinear problems. The book provides useful insights suitable for advanced graduate students, faculty, and researchers in applied and computational mathematics as well as research engineers, mathematical physicists, and systems engineers.

Regularity and Stability for Periodic Solutions to Nonlinear Klein- Gordon and Schrödinger Equations

Author : Xinming Zhao
Publisher :
ISBN 13 :
Total Pages : 186 pages
Book Rating : 4.3/5 (129 download)

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Book Synopsis Regularity and Stability for Periodic Solutions to Nonlinear Klein- Gordon and Schrödinger Equations by : Xinming Zhao

Download or read book Regularity and Stability for Periodic Solutions to Nonlinear Klein- Gordon and Schrödinger Equations written by Xinming Zhao and published by . This book was released on 1996 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Nonlinear Elliptic and Parabolic Problems

Author : Michel Chipot
Publisher : Springer Science & Business Media
ISBN 13 : 9783764372668
Total Pages : 556 pages
Book Rating : 4.3/5 (726 download)

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Book Synopsis Nonlinear Elliptic and Parabolic Problems by : Michel Chipot

Download or read book Nonlinear Elliptic and Parabolic Problems written by Michel Chipot and published by Springer Science & Business Media. This book was released on 2005-10-18 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume is dedicated to celebrate the work of the renowned mathematician Herbert Amann, who had a significant and decisive influence in shaping Nonlinear Analysis. Most articles published in this book, which consists of 32 articles in total, written by highly distinguished researchers, are in one way or another related to the scientific works of Herbert Amann. The contributions cover a wide range of nonlinear elliptic and parabolic equations with applications to natural sciences and engineering. Special topics are fluid dynamics, reaction-diffusion systems, bifurcation theory, maximal regularity, evolution equations, and the theory of function spaces.

Nonlinear Dispersive Equations

Author : Jaime Angulo Pava
Publisher : American Mathematical Soc.
ISBN 13 : 0821848976
Total Pages : 272 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Nonlinear Dispersive Equations by : Jaime Angulo Pava

Download or read book Nonlinear Dispersive Equations written by Jaime Angulo Pava and published by American Mathematical Soc.. This book was released on 2009 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a self-contained presentation of classical and new methods for studying wave phenomena that are related to the existence and stability of solitary and periodic travelling wave solutions for nonlinear dispersive evolution equations. Simplicity, concrete examples, and applications are emphasized throughout in order to make the material easily accessible. The list of classical nonlinear dispersive equations studied include Korteweg-de Vries, Benjamin-Ono, and Schrodinger equations. Many special Jacobian elliptic functions play a role in these examples. The author brings the reader to the forefront of knowledge about some aspects of the theory and motivates future developments in this fascinating and rapidly growing field. The book can be used as an instructive study guide as well as a reference by students and mature scientists interested in nonlinear wave phenomena.