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A Variational Problem Leading To A Singular Elliptic Equation Involving The 1 Laplacian
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Book Synopsis A Variational Problem Leading to a Singular Elliptic Equation Involving the 1-Laplacian by : Florian Krügel
Download or read book A Variational Problem Leading to a Singular Elliptic Equation Involving the 1-Laplacian written by Florian Krügel and published by . This book was released on 2013 with total page 115 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Proceedings of the Conference on Differential & Difference Equations and Applications by : Ravi P. Agarwal
Download or read book Proceedings of the Conference on Differential & Difference Equations and Applications written by Ravi P. Agarwal and published by Hindawi Publishing Corporation. This book was released on 2006 with total page 1268 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 406 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 Computation of Singular Solutions in Elliptic Problems and Elasticity by : D. Leguillon
Download or read book Computation of Singular Solutions in Elliptic Problems and Elasticity written by D. Leguillon and published by John Wiley & Sons. This book was released on 1987 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: The stress field in composite elastic media often contains singularities, in particular at the intersections of interfaces with boundaries. This book describes two new methods of computing the eigenvalues and eigenvectors of singularities, leading to a full description of their structure.
Book Synopsis Oblique Derivative Problems for Elliptic Equations in Conical Domains by : Mikhail Borsuk
Download or read book Oblique Derivative Problems for Elliptic Equations in Conical Domains written by Mikhail Borsuk and published by Springer Nature. This book was released on 2023-05-31 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of our book is the investigation of the behavior of strong and weak solutions to the regular oblique derivative problems for second order elliptic equations, linear and quasi-linear, in the neighborhood of the boundary singularities. The main goal is to establish the precise exponent of the solution decrease rate and under the best possible conditions. The question on the behavior of solutions of elliptic boundary value problems near boundary singularities is of great importance for its many applications, e.g., in hydrodynamics, aerodynamics, fracture mechanics, in the geodesy etc. Only few works are devoted to the regular oblique derivative problems for second order elliptic equations in non-smooth domains. All results are given with complete proofs. The monograph will be of interest to graduate students and specialists in elliptic boundary value problems and their applications.
Book Synopsis Nonlinear Differential Problems with Smooth and Nonsmooth Constraints by : Dumitru Motreanu
Download or read book Nonlinear Differential Problems with Smooth and Nonsmooth Constraints written by Dumitru Motreanu and published by Academic Press. This book was released on 2018-02-05 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Differential Problems with Smooth and Nonsmooth Constraints systematically evaluates how to solve boundary value problems with smooth and nonsmooth constraints. Primarily covering nonlinear elliptic eigenvalue problems and quasilinear elliptic problems using techniques amalgamated from a range of sophisticated nonlinear analysis domains, the work is suitable for PhD and other early career researchers seeking solutions to nonlinear differential equations. Although an advanced work, the book is self-contained, requiring only graduate-level knowledge of functional analysis and topology. Whenever suitable, open problems are stated and partial solutions proposed. The work is accompanied by end-of-chapter problems and carefully curated references. Builds from functional analysis and operator theory, to nonlinear elliptic systems and control problems Outlines the evolution of the main ideas of nonlinear analysis and their roots in classical mathematics Presented with numerous end-of-chapter exercises and sophisticated open problems Illustrated with pertinent industrial and engineering numerical examples and applications Accompanied by hundreds of curated references, saving readers hours of research in conducting literature analysis
Book Synopsis Mathematical Models for Phase Change Problems by : J.F. Rodriques
Download or read book Mathematical Models for Phase Change Problems written by J.F. Rodriques and published by Birkhäuser. This book was released on 2013-03-07 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph collects research and expository articles reflect ing the interaction and the cooperation of different groups in several European institut ions concerning current research on mathematical models for the behaviour of materials with phase change. These papers were presented and discussed in a Workshop held at Obidos, Portugal, du ring the first three days of October, 1988, and grew out of a two year period of intensive exploitation of differ ent abilities and mathematical experiences of the six participating groups, namely, in the University of Augsburg, wh ich was the co ordination center of this project, the Laboratoire Central des Ponts et Chaussees of Paris, the Aristoteles University of Thessaloniki, the University of Florence, the University of Lisbon and the University of Oxford. This project was carried out under the title "Mathemat ical Models of Phase Transitions and Numerical Simulation", in the framework of twinning program for stimulation of cooperation and scientific interchange, sponsored by the European Community. The underlying idea of the project was to create and study the mathematical models arising in applied engineering problems with free boundaries in a broad sense, namely in melting and freezing problems, diffusion-reaction processes, solid-solid phase transition, hysteresis phenomena, "mushy region" descriptions, contact prob lems with friction andjor adhesion, elastoplastic deformations, etc. vi This large spectrum of applied problems have in common the main feature of brusque transitions of their qualitative behaviour that correspond, in general, to non-classical discontinuous monotone or non monotone strong nonlinearities in the mathematical equations
Book Synopsis Lebesgue and Sobolev Spaces with Variable Exponents by : Lars Diening
Download or read book Lebesgue and Sobolev Spaces with Variable Exponents written by Lars Diening and published by Springer. This book was released on 2011-03-29 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of variable exponent function spaces has witnessed an explosive growth in recent years. The standard reference article for basic properties is already 20 years old. Thus this self-contained monograph collecting all the basic properties of variable exponent Lebesgue and Sobolev spaces is timely and provides a much-needed accessible reference work utilizing consistent notation and terminology. Many results are also provided with new and improved proofs. The book also presents a number of applications to PDE and fluid dynamics.
Book Synopsis Solutions of Nonlinear Differential Equations by : Lin Li
Download or read book Solutions of Nonlinear Differential Equations written by Lin Li and published by World Scientific. This book was released on 2016-04-15 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: Variational methods are very powerful techniques in nonlinear analysis and are extensively used in many disciplines of pure and applied mathematics (including ordinary and partial differential equations, mathematical physics, gauge theory, and geometrical analysis). In our first chapter, we gather the basic notions and fundamental theorems that will be applied throughout the chapters. While many of these items are easily available in the literature, we gather them here both for the convenience of the reader and for the purpose of making this volume somewhat self-contained. Subsequent chapters deal with how variational methods can be used in fourth-order problems, Kirchhoff problems, nonlinear field problems, gradient systems, and variable exponent problems. A very extensive bibliography is also included. Contents:PrefaceSome Notations and ConventionsPreliminaries and Variational PrinciplesQuasilinear Fourth-Order ProblemsKirchhoff ProblemsNonlinear Field ProblemsGradient SystemsVariable Exponent Problems Readership: Graduate students and researchers interested in variational methods.
Book Synopsis Elliptic Partial Differential Equations by : Vitaly Volpert
Download or read book Elliptic Partial Differential Equations written by Vitaly Volpert and published by Springer Science & Business Media. This book was released on 2011-03-03 with total page 649 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of elliptic partial differential equations has undergone an important development over the last two centuries. Together with electrostatics, heat and mass diffusion, hydrodynamics and many other applications, it has become one of the most richly enhanced fields of mathematics. This monograph undertakes a systematic presentation of the theory of general elliptic operators. The author discusses a priori estimates, normal solvability, the Fredholm property, the index of an elliptic operator, operators with a parameter, and nonlinear Fredholm operators. Particular attention is paid to elliptic problems in unbounded domains which have not yet been sufficiently treated in the literature and which require some special approaches. The book also contains an analysis of non-Fredholm operators and discrete operators as well as extensive historical and bibliographical comments . The selected topics and the author's level of discourse will make this book a most useful resource for researchers and graduate students working in the broad field of partial differential equations and applications.
Book Synopsis Local And Global Aspects Of Quasilinear Degenerate Elliptic Equations: Quasilinear Elliptic Singular Problems by : Veron Laurent
Download or read book Local And Global Aspects Of Quasilinear Degenerate Elliptic Equations: Quasilinear Elliptic Singular Problems written by Veron Laurent and published by World Scientific. This book was released on 2017-05-05 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the study of elliptic second-order degenerate quasilinear equations, the model of which is the p-Laplacian, with or without dominant lower order reaction term. Emphasis is put on three aspects: The existence of separable singular solutions enables the description of isolated singularities of general solutions. The construction of singular solutions is delicate and cannot be done without the understanding of the spherical p-harmonic eigenvalue problem.When the equations are considered on a Riemannian manifold, existence or non-existence of solutions depends on geometric assumptions such as the curvature. A priori estimates and Liouville type problems are analyzed.When the equations are considered with a forcing term in the class of measures, their study is strongly linked to the properties of a class of potentials appearing in harmonic analysis such as the Riesz, the Bessel or the Wolff potentials and to their associated capacities. Necessary and sufficient conditions for existence of solutions link the continuity of the measure with respect to some appropriate capacity.
Book Synopsis Spectral Problems Associated with Corner Singularities of Solutions to Elliptic Equations by : Vladimir Kozlov
Download or read book Spectral Problems Associated with Corner Singularities of Solutions to Elliptic Equations written by Vladimir Kozlov and published by American Mathematical Soc.. This book was released on 2001 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the analysis of eigenvalues and eigenfunctions that describe singularities of solutions to elliptic boundary value problems in domains with corners and edges. The authors treat both classical problems of mathematical physics and general elliptic boundary value problems. The volume is divided into two parts: The first is devoted to the power-logarithmic singularities of solutions to classical boundary value problems of mathematical physics. The second deals with similar singularities for higher order elliptic equations and systems. Chapter 1 collects basic facts concerning operator pencils acting in a pair of Hilbert spaces. Related properties of ordinary differential equations with constant operator coefficients are discussed and connections with the theory of general elliptic boundary value problems in domains with conic vertices are outlined. New results are presented. Chapter 2 treats the Laplace operator as a starting point and a model for the subsequent study of angular and conic singularities of solutions. Chapter 3 considers the Dirichlet boundary condition beginning with the plane case and turning to the space problems. Chapter 4 investigates some mixed boundary conditions. The Stokes system is discussed in Chapters 5 and 6, and Chapter 7 concludes with the Dirichlet problem for the polyharmonic operator. Chapter 8 studies the Dirichlet problem for general elliptic differential equations of order 2m in an angle. In Chapter 9, an asymptotic formula for the distribution of eigenvalues of operator pencils corresponding to general elliptic boundary value problems in an angle is obtained. Chapters 10 and 11 discuss the Dirichlet problem for elliptic systems of differential equations of order 2 in an n-dimensional cone. Chapter 12 studies the Neumann problem for general elliptic systems, in particular with eigenvalues of the corresponding operator pencil in the strip $\mid {\Re} \lambda - m + /2n \mid \leq 1/2$. It is shown that only integer numbers contained in this strip are eigenvalues. Applications are placed within chapter introductions and as special sections at the end of chapters. Prerequisites include standard PDE and functional analysis courses.
Book Synopsis The obstacle problem by : Luis Angel Caffarelli
Download or read book The obstacle problem written by Luis Angel Caffarelli and published by Edizioni della Normale. This book was released on 1999-10-01 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The material presented here corresponds to Fermi lectures that I was invited to deliver at the Scuola Normale di Pisa in the spring of 1998. The obstacle problem consists in studying the properties of minimizers of the Dirichlet integral in a domain D of Rn, among all those configurations u with prescribed boundary values and costrained to remain in D above a prescribed obstacle F. In the Hilbert space H1(D) of all those functions with square integrable gradient, we consider the closed convex set K of functions u with fixed boundary value and which are greater than F in D. There is a unique point in K minimizing the Dirichlet integral. That is called the solution to the obstacle problem.
Author :Giovanni Maria Troianiello Publisher :Springer Science & Business Media ISBN 13 :9780306424489 Total Pages :378 pages Book Rating :4.4/5 (244 download)
Book Synopsis Elliptic Differential Equations and Obstacle Problems by : Giovanni Maria Troianiello
Download or read book Elliptic Differential Equations and Obstacle Problems written by Giovanni Maria Troianiello and published by Springer Science & Business Media. This book was released on 1987-07-31 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the few years since their appearance in the mid-sixties, variational inequalities have developed to such an extent and so thoroughly that they may now be considered an "institutional" development of the theory of differential equations (with appreciable feedback as will be shown). This book was written in the light of these considerations both in regard to the choice of topics and to their treatment. In short, roughly speaking my intention was to write a book on second-order elliptic operators, with the first half of the book, as might be expected, dedicated to function spaces and to linear theory whereas the second, nonlinear half would deal with variational inequalities and non variational obstacle problems, rather than, for example, with quasilinear or fully nonlinear equations (with a few exceptions to which I shall return later). This approach has led me to omit any mention of "physical" motivations in the wide sense of the term, in spite of their historical and continuing importance in the development of variational inequalities. I here addressed myself to a potential reader more or less aware of the significant role of variational inequalities in numerous fields of applied mathematics who could use an analytic presentation of the fundamental theory, which would be as general and self-contained as possible.
Download or read book Mathematical Reviews written by and published by . This book was released on 2008 with total page 866 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis One-dimensional Variational Problems by : Giuseppe Buttazzo
Download or read book One-dimensional Variational Problems written by Giuseppe Buttazzo and published by Oxford University Press. This book was released on 1998 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: While easier to solve and accessible to a broader range of students, one-dimensional variational problems and their associated differential equations exhibit many of the same complex behavior of higher-dimensional problems. This book, the first moden introduction, emphasizes direct methods and provides an exceptionally clear view of the underlying theory.
Book Synopsis Geometric Properties for Parabolic and Elliptic PDE's by : Rolando Magnanini
Download or read book Geometric Properties for Parabolic and Elliptic PDE's written by Rolando Magnanini and published by Springer Science & Business Media. This book was released on 2012-11-27 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of qualitative aspects of PDE's has always attracted much attention from the early beginnings. More recently, once basic issues about PDE's, such as existence, uniqueness and stability of solutions, have been understood quite well, research on topological and/or geometric properties of their solutions has become more intense. The study of these issues is attracting the interest of an increasing number of researchers and is now a broad and well-established research area, with contributions that often come from experts from disparate areas of mathematics, such as differential and convex geometry, functional analysis, calculus of variations, mathematical physics, to name a few. This volume collects a selection of original results and informative surveys by a group of international specialists in the field, analyzes new trends and techniques and aims at promoting scientific collaboration and stimulating future developments and perspectives in this very active area of research.
