Elliptic Partial Differential Equations From An Elementary Viewpoint A Fresh Glance At The Classical Theory
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Elliptic Partial Differential Equations From An Elementary Viewpoint A Fresh Glance At The Classical Theory
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Author : Serena Dipierro
language : en
Publisher: World Scientific
Release Date : 2024-07-02
Elliptic Partial Differential Equations From An Elementary Viewpoint A Fresh Glance At The Classical Theory written by Serena Dipierro and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-02 with Mathematics categories.
This is a textbook that covers several selected topics in the theory of elliptic partial differential equations which can be used in an advanced undergraduate or graduate course.The book considers many important issues such as existence, regularity, qualitative properties, and all the classical topics useful in the wide world of partial differential equations. It also includes applications with interesting examples.The structure of the book is flexible enough to allow different chapters to be taught independently.The book is friendly, welcoming, and written for a newcomer to the subject.It is essentially self-contained, making it easy to read, and all the concepts are fully explained from scratch, combining intuition and rigor, and therefore it can also be read independently by students, with limited or no supervision.
Subject Guide To Books In Print
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Author :
language : en
Publisher:
Release Date : 1991
Subject Guide To Books In Print written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with American literature categories.
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.
Partial Differential Equations Of Elliptic Type
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Author : C. Miranda
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Partial Differential Equations Of Elliptic Type written by C. Miranda 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 2012-12-06 with Mathematics categories.
In the theory of partial differential equations, the study of elliptic equations occupies a preeminent position, both because of the importance which it assumes for various questions in mathematical physics, and because of the completeness of the results obtained up to the present time. In spite of this, even in the more classical treatises on analysis the theory of elliptic equations has been considered and illustrated only from particular points of view, while the only expositions of the whole theory, the extremely valuable ones by LICHTENSTEIN and AscoLI, have the charac ter of encyclopedia articles and date back to many years ago. Consequently it seemed to me that it would be of some interest to try to give an up-to-date picture of the present state of research in this area in a monograph which, without attaining the dimensions of a treatise, would nevertheless be sufficiently extensive to allow the expo sition, in some cases in summary form, of the various techniques used in the study of these equations.
Elliptic Partial Differential Equations And Quasiconformal Mappings In The Plane Pms 48
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Author : Kari Astala
language : en
Publisher: Princeton University Press
Release Date : 2009-01-18
Elliptic Partial Differential Equations And Quasiconformal Mappings In The Plane Pms 48 written by Kari Astala and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-01-18 with Mathematics categories.
This book explores the most recent developments in the theory of planar quasiconformal mappings with a particular focus on the interactions with partial differential equations and nonlinear analysis. It gives a thorough and modern approach to the classical theory and presents important and compelling applications across a spectrum of mathematics: dynamical systems, singular integral operators, inverse problems, the geometry of mappings, and the calculus of variations. It also gives an account of recent advances in harmonic analysis and their applications in the geometric theory of mappings. The book explains that the existence, regularity, and singular set structures for second-order divergence-type equations--the most important class of PDEs in applications--are determined by the mathematics underpinning the geometry, structure, and dimension of fractal sets; moduli spaces of Riemann surfaces; and conformal dynamical systems. These topics are inextricably linked by the theory of quasiconformal mappings. Further, the interplay between them allows the authors to extend classical results to more general settings for wider applicability, providing new and often optimal answers to questions of existence, regularity, and geometric properties of solutions to nonlinear systems in both elliptic and degenerate elliptic settings.
Stable Solutions Of Elliptic Partial Differential Equations
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Author : Louis Dupaigne
language : en
Publisher: CRC Press
Release Date : 2011-03-15
Stable Solutions Of Elliptic Partial Differential Equations written by Louis Dupaigne and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-15 with Mathematics categories.
Stable solutions are ubiquitous in differential equations. They represent meaningful solutions from a physical point of view and appear in many applications, including mathematical physics (combustion, phase transition theory) and geometry (minimal surfaces). Stable Solutions of Elliptic Partial Differential Equations offers a self-contained presentation of the notion of stability in elliptic partial differential equations (PDEs). The central questions of regularity and classification of stable solutions are treated at length. Specialists will find a summary of the most recent developments of the theory, such as nonlocal and higher-order equations. For beginners, the book walks you through the fine versions of the maximum principle, the standard regularity theory for linear elliptic equations, and the fundamental functional inequalities commonly used in this field. The text also includes two additional topics: the inverse-square potential and some background material on submanifolds of Euclidean space.
Foundations Of The Classical Theory Of Partial Differential Equations
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Author : Yu.V. Egorov
language : en
Publisher:
Release Date : 1998
Foundations Of The Classical Theory Of Partial Differential Equations written by Yu.V. Egorov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.
Elliptic Regularity Theory
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Author : Lisa Beck
language : en
Publisher: Springer
Release Date : 2016-04-08
Elliptic Regularity Theory written by Lisa Beck and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-08 with Mathematics categories.
These lecture notes provide a self-contained introduction to regularity theory for elliptic equations and systems in divergence form. After a short review of some classical results on everywhere regularity for scalar-valued weak solutions, the presentation focuses on vector-valued weak solutions to a system of several coupled equations. In the vectorial case, weak solutions may have discontinuities and so are expected, in general, to be regular only outside of a set of measure zero. Several methods are presented concerning the proof of such partial regularity results, and optimal regularity is discussed. Finally, a short overview is given on the current state of the art concerning the size of the singular set on which discontinuities may occur. The notes are intended for graduate and postgraduate students with a solid background in functional analysis and some familiarity with partial differential equations; they will also be of interest to researchers working on related topics.
Elliptic Partial Differential Equations Of Second Order
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Author : David Gilbarg
language : en
Publisher: Springer
Release Date : 2015-03-30
Elliptic Partial Differential Equations Of Second Order written by David Gilbarg and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-30 with Mathematics categories.
From the reviews: "This is a book of interest to any having to work with differential equations, either as a reference or as a book to learn from. The authors have taken trouble to make the treatment self-contained. It (is) suitable required reading for a PhD student. Although the material has been developed from lectures at Stanford, it has developed into an almost systematic coverage that is much longer than could be covered in a year's lectures". Newsletter, New Zealand Mathematical Society, 1985 " ... as should be clear from the previous discussion, this book is a bibliographical monument to the theory of both theoretical and applied PDEs that has not acquired any flaws due to its age. On the contrary, it remains a crucial and essential tool for the active research in the field. In a few words, in my modest opinion, “. . . this book contains the essential background that a researcher in elliptic PDEs should possess the day s/he gets a permanent academic position. . . .” SIAM Newsletter
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.