Elliptic And Parabolic Equations
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Elliptic Parabolic Equations
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Author : Zhuoqun Wu
language : en
Publisher: World Scientific
Release Date : 2006
Elliptic Parabolic Equations written by Zhuoqun Wu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
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.
Second Order Equations Of Elliptic And Parabolic Type
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Author : E. M. Landis
language : en
Publisher: American Mathematical Soc.
Release Date : 1997-12-02
Second Order Equations Of Elliptic And Parabolic Type written by E. M. Landis 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 1997-12-02 with Mathematics categories.
Most books on elliptic and parabolic equations emphasize existence and uniqueness of solutions. By contrast, this book focuses on the qualitative properties of solutions. In addition to the discussion of classical results for equations with smooth coefficients (Schauder estimates and the solvability of the Dirichlet problem for elliptic equations; the Dirichlet problem for the heat equation), the book describes properties of solutions to second order elliptic and parabolic equations with measurable coefficients near the boundary and at infinity. The book presents a fine elementary introduction to the theory of elliptic and parabolic equations of second order. The precise and clear exposition is suitable for graduate students as well as for research mathematicians who want to get acquainted with this area of the theory of partial differential equations.
Elliptic And Parabolic Equations With Discontinuous Coefficients
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Author : Antonino Maugeri
language : en
Publisher: Wiley-VCH
Release Date : 2000-12-13
Elliptic And Parabolic Equations With Discontinuous Coefficients written by Antonino Maugeri and has been published by Wiley-VCH this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-12-13 with Mathematics categories.
This book unifies the different approaches in studying elliptic and parabolic partial differential equations with discontinuous coefficients. To the enlarging market of researchers in applied sciences, mathematics and physics, it gives concrete answers to questions suggested by non-linear models. Providing an up-to date survey on the results concerning elliptic and parabolic operators on a high level, the authors serve the reader in doing further research. Being themselves active researchers in the field, the authors describe both on the level of good examples and precise analysis, the crucial role played by such requirements on the coefficients as the Cordes condition, Campanato's nearness condition, and vanishing mean oscillation condition. They present the newest results on the basic boundary value problems for operators with VMO coefficients and non-linear operators with discontinuous coefficients and state a lot of open problems in the field.
Quasilinear Degenerate And Nonuniformly Elliptic And Parabolic Equations Of Second Order
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Author : A. V. Ivanov
language : en
Publisher: American Mathematical Soc.
Release Date : 1984
Quasilinear Degenerate And Nonuniformly Elliptic And Parabolic Equations Of Second Order written by A. V. Ivanov 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 1984 with Mathematics categories.
Lectures On Elliptic And Parabolic Equations In H Lder Spaces
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Author : Nikolaĭ Vladimirovich Krylov
language : en
Publisher: American Mathematical Soc.
Release Date : 1996
Lectures On Elliptic And Parabolic Equations In H Lder Spaces written by Nikolaĭ Vladimirovich Krylov 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 1996 with Mathematics categories.
These lectures concentrate on fundamentals of the modern theory of linear elliptic and parabolic equations in H older spaces. Krylov shows that this theory - including some issues of the theory of nonlinear equations - is based on some general and extremely powerful ideas and some simple computations. The main object of study is the first boundary-value problems for elliptic and parabolic equations, with some guidelines concerning other boundary-value problems such as the Neumann or oblique derivative problems or problems involving higher-order elliptic operators acting on the boundary. Numerical approximations are also discussed. This book, containing 200 exercises, aims to provide a good understanding of what kind of results are available and what kinds of techniques are used to obtain them.
Nonlinear Elliptic And Parabolic Equations Of The Second Order
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Author : N.V. Krylov
language : en
Publisher: Springer
Release Date : 2001-11-30
Nonlinear Elliptic And Parabolic Equations Of The Second Order written by N.V. Krylov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-11-30 with Mathematics categories.
Approach your problems from the It isn't that they can't see the right end and begin with the solution. It is that they can't see answers. Then one day, perhaps the problem. you will find the final question. G.K. Chesterton. The Scandal of 'The Hermit Clad in Crane Father Brown 'The Point of a Pin'. Feathers' in R. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of mono graphs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theor.etical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces.
Singular Solutions Of Nonlinear Elliptic And Parabolic Equations
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Author : Alexander A. Kovalevsky
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2016-03-21
Singular Solutions Of Nonlinear Elliptic And Parabolic Equations written by Alexander A. Kovalevsky and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-21 with Mathematics categories.
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
Elliptic And Parabolic Equations Involving The Hardy Leray Potential
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Author : Ireneo Peral Alonso
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2021-02-22
Elliptic And Parabolic Equations Involving The Hardy Leray Potential written by Ireneo Peral Alonso and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-22 with Mathematics categories.
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.
Lectures On Elliptic And Parabolic Equations In Sobolev Spaces
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Author : Nikolaĭ Vladimirovich Krylov
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Lectures On Elliptic And Parabolic Equations In Sobolev Spaces written by Nikolaĭ Vladimirovich Krylov 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 2008 with Differential equations, Elliptic categories.
This book concentrates on the basic facts and ideas of the modern theory of linear elliptic and parabolic equations in Sobolev spaces. The main areas covered in this book are the first boundary-value problem for elliptic equations and the Cauchy problem for parabolic equations. In addition, other boundary-value problems such as the Neumann or oblique derivative problems are briefly covered. As is natural for a textbook, the main emphasis is on organizing well-known ideas in a self-contained exposition. Among the topics included that are not usually covered in a textbook are a relatively recent development concerning equations with $\textsf{VMO}$ coefficients and the study of parabolic equations with coefficients measurable only with respect to the time variable. There are numerous exercises which help the reader better understand the material. After going through the book, the reader will have a good understanding of results available in the modern theory of partial differential equations and the technique used to obtain them. Prerequesites are basics of measure theory, the theory of $L p$ spaces, and the Fourier transform.
Numerical Methods For Elliptic And Parabolic Partial Differential Equations
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Author : Peter Knabner
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-05-26
Numerical Methods For Elliptic And Parabolic Partial Differential Equations written by Peter Knabner 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 2006-05-26 with Mathematics categories.
This text provides an application oriented introduction to the numerical methods for partial differential equations. It covers finite difference, finite element, and finite volume methods, interweaving theory and applications throughout. The book examines modern topics such as adaptive methods, multilevel methods, and methods for convection-dominated problems and includes detailed illustrations and extensive exercises.