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Degenerate Elliptic And Parabolic Equations And Variational Inequalities
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Book Synopsis Degenerate Elliptic Equations by : Serge Levendorskii
Download or read book Degenerate Elliptic Equations written by Serge Levendorskii and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the first to be devoted to the study of various properties of wide classes of degenerate elliptic operators of arbitrary order and pseudo-differential operators with multiple characteristics. Conditions for operators to be Fredholm in appropriate weighted Sobolev spaces are given, a priori estimates of solutions are derived, inequalities of the Grding type are proved, and the principal term of the spectral asymptotics for self-adjoint operators is computed. A generalization of the classical Weyl formula is proposed. Some results are new, even for operators of the second order. In addition, an analogue of the Boutet de Monvel calculus is developed and the index is computed. For postgraduate and research mathematicians, physicists and engineers whose work involves the solution of partial differential equations.
Book Synopsis Elliptic & Parabolic Equations by : Zhuoqun Wu
Download or read book Elliptic & Parabolic Equations written by Zhuoqun Wu and published by World Scientific. This book was released on 2006 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to elliptic and parabolic equations. While there are numerous monographs focusing separately on each kind of equations, there are very few books treating these two kinds of equations in combination. This book presents the related basic theories and methods to enable readers to appreciate the commonalities between these two kinds of equations as well as contrast the similarities and differences between them.
Book Synopsis Elliptic and Parabolic Problems by : C Bandle
Download or read book Elliptic and Parabolic Problems written by C Bandle and published by CRC Press. This book was released on 2020-11-26 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Research Note presents some recent advances in various important domains of partial differential equations and applied mathematics including equations and systems of elliptic and parabolic type and various applications in physics, mechanics and engineering. These topics are now part of various areas of science and have experienced tremendous development during the last decades. -------------------------------------
Book Synopsis Regularity Estimates for Nonlinear Elliptic and Parabolic Problems by : John Lewis
Download or read book Regularity Estimates for Nonlinear Elliptic and Parabolic Problems written by John Lewis and published by Springer Science & Business Media. This book was released on 2012-03-02 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: The issue of regularity has played a central role in the theory of Partial Differential Equations almost since its inception, and despite the tremendous advances made it still remains a very fruitful research field. In particular considerable strides have been made in regularity estimates for degenerate and singular elliptic and parabolic equations over the last several years, and in many unexpected and challenging directions. Because of all these recent results, it seemed high time to create an overview that would highlight emerging trends and issues in this fascinating research topic in a proper and effective way. The course aimed to show the deep connections between these topics and to open new research directions through the contributions of leading experts in all of these fields.
Book Synopsis Quasilinear Degenerate and Nonuniformly Elliptic and Parabolic Equations of Second Order by : A. V. Ivanov
Download or read book Quasilinear Degenerate and Nonuniformly Elliptic and Parabolic Equations of Second Order written by A. V. Ivanov and published by American Mathematical Soc.. This book was released on 1984 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Degenerate Differential Equations in Banach Spaces by : Angelo Favini
Download or read book Degenerate Differential Equations in Banach Spaces written by Angelo Favini and published by CRC Press. This book was released on 1998-09-10 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work presents a detailed study of linear abstract degenerate differential equations, using both the semigroups generated by multivalued (linear) operators and extensions of the operational method from Da Prato and Grisvard. The authors describe the recent and original results on PDEs and algebraic-differential equations, and establishes the analyzability of the semigroup generated by some degenerate parabolic operators in spaces of continuous functions.
Book Synopsis Convex Analysis and Nonlinear Geometric Elliptic Equations by : Ilya J. Bakelman
Download or read book Convex Analysis and Nonlinear Geometric Elliptic Equations written by Ilya J. Bakelman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: Investigations in modem nonlinear analysis rely on ideas, methods and prob lems from various fields of mathematics, mechanics, physics and other applied sciences. In the second half of the twentieth century many prominent, ex emplary problems in nonlinear analysis were subject to intensive study and examination. The united ideas and methods of differential geometry, topology, differential equations and functional analysis as well as other areas of research in mathematics were successfully applied towards the complete solution of com plex problems in nonlinear analysis. It is not possible to encompass in the scope of one book all concepts, ideas, methods and results related to nonlinear analysis. Therefore, we shall restrict ourselves in this monograph to nonlinear elliptic boundary value problems as well as global geometric problems. In order that we may examine these prob lems, we are provided with a fundamental vehicle: The theory of convex bodies and hypersurfaces. In this book we systematically present a series of centrally significant results obtained in the second half of the twentieth century up to the present time. Particular attention is given to profound interconnections between various divisions in nonlinear analysis. The theory of convex functions and bodies plays a crucial role because the ellipticity of differential equations is closely connected with the local and global convexity properties of their solutions. Therefore it is necessary to have a sufficiently large amount of material devoted to the theory of convex bodies and functions and their connections with partial differential equations.
Author :Emmanuele DiBenedetto Publisher :Springer Science & Business Media ISBN 13 :1461208955 Total Pages :402 pages Book Rating :4.4/5 (612 download)
Book Synopsis Degenerate Parabolic Equations by : Emmanuele DiBenedetto
Download or read book Degenerate Parabolic Equations written by Emmanuele DiBenedetto and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Evolved from the author's lectures at the University of Bonn's Institut für angewandte Mathematik, this book reviews recent progress toward understanding of the local structure of solutions of degenerate and singular parabolic partial differential equations.
Book Synopsis Convex Analysis and Variational Problems by : Ivar Ekeland
Download or read book Convex Analysis and Variational Problems written by Ivar Ekeland and published by SIAM. This book was released on 1999-12-01 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains different developments of infinite dimensional convex programming in the context of convex analysis, including duality, minmax and Lagrangians, and convexification of nonconvex optimization problems in the calculus of variations (infinite dimension). It also includes the theory of convex duality applied to partial differential equations; no other reference presents this in a systematic way. The minmax theorems contained in this book have many useful applications, in particular the robust control of partial differential equations in finite time horizon. First published in English in 1976, this SIAM Classics in Applied Mathematics edition contains the original text along with a new preface and some additional references.
Book Synopsis Recent Advances In Nonlinear Analysis - Proceedings Of The International Conference On Nonlinear Analysis by : Michel Marie Chipot
Download or read book Recent Advances In Nonlinear Analysis - Proceedings Of The International Conference On Nonlinear Analysis written by Michel Marie Chipot and published by World Scientific. This book was released on 2008-02-22 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume considers the most recent advances in various topics in partial differential equations. Many important issues such as evolution problems, their asymptotic behavior and their qualitative properties are addressed. The quality and completeness of the articles make this book both a source of inspiration and reference for future research.
Book Synopsis Stochastic Differential Equations and Applications by : Avner Friedman
Download or read book Stochastic Differential Equations and Applications written by Avner Friedman and published by Academic Press. This book was released on 2014-06-20 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic Differential Equations and Applications, Volume 2 is an eight-chapter text that focuses on the practical aspects of stochastic differential equations. This volume begins with a presentation of the auxiliary results in partial differential equations that are needed in the sequel. The succeeding chapters describe the behavior of the sample paths of solutions of stochastic differential equations. These topics are followed by a consideration of an issue whether the paths can hit a given set with positive probability, as well as the stability of paths about a given manifold and with spiraling of paths about this manifold. Other chapters deal with the applications to partial equations, specifically with the Dirichlet problem for degenerate elliptic equations. These chapters also explore the questions of singular perturbations and the existence of fundamental solutions for degenerate parabolic equations. The final chapters discuss stopping time problems, stochastic games, and stochastic differential games. This book is intended primarily to undergraduate and graduate mathematics students.
Book Synopsis Applied Analysis: Mathematics For Science, Technology, Engineering (Third Edition) by : Takashi Suzuki
Download or read book Applied Analysis: Mathematics For Science, Technology, Engineering (Third Edition) written by Takashi Suzuki and published by World Scientific. This book was released on 2022-04-28 with total page 688 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is to be a new edition of Applied Analysis. Several fundamental materials of applied and theoretical sciences are added, which are needed by the current society, as well as recent developments in pure and applied mathematics. New materials in the basic level are the mathematical modelling using ODEs in applied sciences, elements in Riemann geometry in accordance with tensor analysis used in continuum mechanics, combining engineering and modern mathematics, detailed description of optimization, and real analysis used in the recent study of PDEs. Those in the advance level are the integration of ODEs, inverse Strum Liouville problems, interface vanishing of the Maxwell system, method of gradient inequality, diffusion geometry, mathematical oncology. Several descriptions on the analysis of Smoluchowski-Poisson equation in two space dimension are corrected and extended, to ensure quantized blowup mechanism of this model, particularly, the residual vanishing both in blowup solution in finite time with possible collision of sub-collapses and blowup solutions in infinite time without it.
Book Synopsis Elliptic Boundary Value Problems of Second Order in Piecewise Smooth Domains by : Michail Borsuk
Download or read book Elliptic Boundary Value Problems of Second Order in Piecewise Smooth Domains written by Michail Borsuk and published by Elsevier. This book was released on 2006-01-12 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book contains a systematic treatment of the qualitative theory of elliptic boundary value problems for linear and quasilinear second order equations in non-smooth domains. The authors concentrate on the following fundamental results: sharp estimates for strong and weak solutions, solvability of the boundary value problems, regularity assertions for solutions near singular points.Key features:* New the Hardy – Friedrichs – Wirtinger type inequalities as well as new integral inequalities related to the Cauchy problem for a differential equation.* Precise exponents of the solution decreasing rate near boundary singular points and best possible conditions for this.* The question about the influence of the coefficients smoothness on the regularity of solutions.* New existence theorems for the Dirichlet problem for linear and quasilinear equations in domains with conical points.* The precise power modulus of continuity at singular boundary point for solutions of the Dirichlet, mixed and the Robin problems.* The behaviour of weak solutions near conical point for the Dirichlet problem for m – Laplacian.* The behaviour of weak solutions near a boundary edge for the Dirichlet and mixed problem for elliptic quasilinear equations with triple degeneration.* Precise exponents of the solution decreasing rate near boundary singular points and best possible conditions for this.* The question about the influence of the coefficients smoothness on the regularity of solutions.* New existence theorems for the Dirichlet problem for linear and quasilinear equations in domains with conical points.* The precise power modulus of continuity at singular boundary point for solutions of the Dirichlet, mixed and the Robin problems.* The behaviour of weak solutions near conical point for the Dirichlet problem for m - Laplacian.* The behaviour of weak solutions near a boundary edge for the Dirichlet and mixed problem for elliptic quasilinear equations with triple degeneration.
Book Synopsis Convex Analysis and Variational Problems by :
Download or read book Convex Analysis and Variational Problems written by and published by Elsevier. This book was released on 1976-01-01 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: Convex Analysis and Variational Problems
Book Synopsis Harnack Inequalities and Nonlinear Operators by : Vincenzo Vespri
Download or read book Harnack Inequalities and Nonlinear Operators written by Vincenzo Vespri and published by Springer Nature. This book was released on 2021-05-29 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book contains two contributions about the work of Emmanuele DiBenedetto and a selection of original papers. The authors are some of the main experts in Harnack’s inequalities and nonlinear operators. These papers are part of the contributions presented during the conference to celebrate the 70th birthday of Prof. Emmanuele DiBenedetto, which was held at “Il Palazzone” in Cortona from June 18th to 24th, 2017. The papers are focused on current research topics regarding the qualitative properties of solutions, connections with calculus of variations, Harnack inequality and regularity theory. Some papers are also related to various applications. Many of the authors have shared with Prof. DiBenedetto an intense scientific and personal collaboration, while many others have taken inspiration from and further developed his field of research. The topics of the conference are certainly of great interest for the international mathematical community.
Book Synopsis Elliptic and Parabolic Equations Involving the Hardy-Leray Potential by : Ireneo Peral Alonso
Download or read book Elliptic and Parabolic Equations Involving the Hardy-Leray Potential written by Ireneo Peral Alonso and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-02-22 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: The scientific literature on the Hardy-Leray inequality, also known as the uncertainty principle, is very extensive and scattered. The Hardy-Leray potential shows an extreme spectral behavior and a peculiar influence on diffusion problems, both stationary and evolutionary. In this book, a big part of the scattered knowledge about these different behaviors is collected in a unified and comprehensive presentation.
Book Synopsis Handbook of Differential Equations: Stationary Partial Differential Equations by : Michel Chipot
Download or read book Handbook of Differential Equations: Stationary Partial Differential Equations written by Michel Chipot and published by Elsevier. This book was released on 2007-05-03 with total page 627 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of self contained state-of-the art surveys. The authors have made an effort to achieve readability for mathematicians and scientists from other fields, for this series of handbooks to be a new reference for research, learning and teaching.- written by well-known experts in the field- self contained volume in series covering one of the most rapid developing topics in mathematics
