Nonlinear Elliptic Partial Differential Equations
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Nonlinear Elliptic Partial Differential Equations
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Author : Hervé Le Dret
language : en
Publisher: Springer
Release Date : 2018-05-25
Nonlinear Elliptic Partial Differential Equations written by Hervé Le Dret and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-25 with Mathematics categories.
This textbook presents the essential parts of the modern theory of nonlinear partial differential equations, including the calculus of variations. After a short review of results in real and functional analysis, the author introduces the main mathematical techniques for solving both semilinear and quasilinear elliptic PDEs, and the associated boundary value problems. Key topics include infinite dimensional fixed point methods, the Galerkin method, the maximum principle, elliptic regularity, and the calculus of variations. Aimed at graduate students and researchers, this textbook contains numerous examples and exercises and provides several comments and suggestions for further study.
Elliptic Partial Differential Equations
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Author : Lucio Boccardo
language : en
Publisher: Walter de Gruyter
Release Date : 2013-10-29
Elliptic Partial Differential Equations written by Lucio Boccardo and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-29 with Mathematics categories.
Elliptic partial differential equations is one of the main and most active areas in mathematics. This book is devoted to the study of linear and nonlinear elliptic problems in divergence form, with the aim of providing classical results, as well as more recent developments about distributional solutions. For this reason this monograph is addressed to master's students, PhD students and anyone who wants to begin research in this mathematical field.
Nonlinear Partial Differential Equations With Applications
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Author : Tomás Roubicek
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-01-17
Nonlinear Partial Differential Equations With Applications written by Tomás Roubicek and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-17 with Mathematics categories.
This book primarily concerns quasilinear and semilinear elliptic and parabolic partial differential equations, inequalities, and systems. The exposition quickly leads general theory to analysis of concrete equations, which have specific applications in such areas as electrically (semi-) conductive media, modeling of biological systems, and mechanical engineering. Methods of Galerkin or of Rothe are exposed in a large generality.
Fully Nonlinear Elliptic Equations
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Author : Luis A. Caffarelli
language : en
Publisher: American Mathematical Soc.
Release Date : 1995
Fully Nonlinear Elliptic Equations written by Luis A. Caffarelli and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
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.
Elliptic Partial Differential Equations
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Author : Qing Han
language : en
Publisher: American Mathematical Soc.
Release Date : 2011
Elliptic Partial Differential Equations written by Qing Han and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
This volume is based on PDE courses given by the authors at the Courant Institute and at the University of Notre Dame, Indiana. Presented are basic methods for obtaining various a priori estimates for second-order equations of elliptic type with particular emphasis on maximal principles, Harnack inequalities, and their applications. The equations considered in the book are linear; however, the presented methods also apply to nonlinear problems.
Lectures On Elliptic Partial Differential Equations
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Author : Luigi Ambrosio
language : en
Publisher: Springer
Release Date : 2019-01-10
Lectures On Elliptic Partial Differential Equations written by Luigi Ambrosio and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-10 with Mathematics categories.
The book originates from the Elliptic PDE course given by the first author at the Scuola Normale Superiore in recent years. It covers the most classical aspects of the theory of Elliptic Partial Differential Equations and Calculus of Variations, including also more recent developments on partial regularity for systems and the theory of viscosity solutions.
Elliptic Equations An Introductory Course
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Author : Michel Chipot
language : en
Publisher: Springer Nature
Release Date : 2024-07-14
Elliptic Equations An Introductory Course written by Michel Chipot and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-14 with Mathematics categories.
The aim of this book is to introduce the reader to different topics of the theory of elliptic partial differential equations by avoiding technicalities and complicated refinements. Apart from the basic theory of equations in divergence form, it includes subjects as singular perturbations, homogenization, computations, asymptotic behavior of problems in cylinders, elliptic systems, nonlinear problems, regularity theory, Navier-Stokes systems, p-Laplace type operators, large solutions, and mountain pass techniques. Just a minimum on Sobolev spaces has been introduced and work on integration on the boundary has been carefully avoided to keep the reader attention focused on the beauty and variety of these issues. The chapters are relatively independent of each other and can be read or taught separately. Numerous results presented here are original, and have not been published elsewhere. The book will be of interest to graduate students and researchers specializing in partial differential equations.
Regularity Results For Nonlinear Elliptic Systems And Applications
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Author : Alain Bensoussan
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Regularity Results For Nonlinear Elliptic Systems And Applications written by Alain Bensoussan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
The book collects many techniques that are helpul in obtaining regularity results for solutions of nonlinear systems of partial differential equations. They are then applied in various cases to provide useful examples and relevant results, particularly in fields like fluid mechanics, solid mechanics, semiconductor theory, or game theory. In general, these techniques are scattered in the journal literature and developed in the strict context of a given model. In the book, they are presented independently of specific models, so that the main ideas are explained, while remaining applicable to various situations. Such a presentation will facilitate application and implementation by researchers, as well as teaching to students.
Elliptic Partial Differential Equations
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Author : Vitaly Volpert
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-03-03
Elliptic Partial Differential Equations written by Vitaly Volpert and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-03 with Mathematics categories.
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.