Elliptic And Parabolic Equations With Discontinuous Coefficients

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Elliptic and Parabolic Equations with Discontinuous Coefficients

Antonino Maugeri,Dian K. Palagachev,Lubomira G. Softova
Elliptic and Parabolic Equations with Discontinuous Coefficients Book PDF

Author : Antonino Maugeri,Dian K. Palagachev,Lubomira G. Softova
Publisher : Wiley-VCH
Page : 266 pages
File Size : 40,5 Mb
Release : 2000-12-13
Category : Mathematics
ISBN : STANFORD:36105110135253

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Elliptic and Parabolic Equations with Discontinuous Coefficients by Antonino Maugeri,Dian K. Palagachev,Lubomira G. Softova Pdf

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.

Sobolev and Viscosity Solutions for Fully Nonlinear Elliptic and Parabolic Equations

N. V. Krylov
Sobolev and Viscosity Solutions for Fully Nonlinear Elliptic and Parabolic Equations Book PDF

Author : N. V. Krylov
Publisher : American Mathematical Soc.
Page : 441 pages
File Size : 43,8 Mb
Release : 2018-09-07
Category : Differential equations, Parabolic
ISBN : 9781470447403

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Sobolev and Viscosity Solutions for Fully Nonlinear Elliptic and Parabolic Equations by N. V. Krylov Pdf

This book concentrates on first boundary-value problems for fully nonlinear second-order uniformly elliptic and parabolic equations with discontinuous coefficients. We look for solutions in Sobolev classes, local or global, or for viscosity solutions. Most of the auxiliary results, such as Aleksandrov's elliptic and parabolic estimates, the Krylov–Safonov and the Evans–Krylov theorems, are taken from old sources, and the main results were obtained in the last few years. Presentation of these results is based on a generalization of the Fefferman–Stein theorem, on Fang-Hua Lin's like estimates, and on the so-called “ersatz” existence theorems, saying that one can slightly modify “any” equation and get a “cut-off” equation that has solutions with bounded derivatives. These theorems allow us to prove the solvability in Sobolev classes for equations that are quite far from the ones which are convex or concave with respect to the Hessians of the unknown functions. In studying viscosity solutions, these theorems also allow us to deal with classical approximating solutions, thus avoiding sometimes heavy constructions from the usual theory of viscosity solutions.

Elliptic & Parabolic Equations

Zhuoqun Wu,Jingxue Yin,Chunpeng Wang
Elliptic Parabolic Equations Book PDF

Author : Zhuoqun Wu,Jingxue Yin,Chunpeng Wang
Publisher : World Scientific
Page : 428 pages
File Size : 54,5 Mb
Release : 2006
Category : Mathematics
ISBN : 9789812700254

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Elliptic & Parabolic Equations by Zhuoqun Wu,Jingxue Yin,Chunpeng Wang Pdf

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.

Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations

Beatrice Riviere
Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations Book PDF

Author : Beatrice Riviere
Publisher : SIAM
Page : 201 pages
File Size : 42,9 Mb
Release : 2008-12-18
Category : Mathematics
ISBN : 9780898716566

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Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations by Beatrice Riviere Pdf

Focuses on three primal DG methods, covering both theory and computation, and providing the basic tools for analysis.

Semigroups of Bounded Operators and Second-Order Elliptic and Parabolic Partial Differential Equations

Luca Lorenzi,Adbelaziz Rhandi
Semigroups of Bounded Operators and Second Order Elliptic and Parabolic Partial Differential Equations Book PDF

Author : Luca Lorenzi,Adbelaziz Rhandi
Publisher : CRC Press
Page : 350 pages
File Size : 55,6 Mb
Release : 2021-01-06
Category : Mathematics
ISBN : 9780429557668

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Semigroups of Bounded Operators and Second-Order Elliptic and Parabolic Partial Differential Equations by Luca Lorenzi,Adbelaziz Rhandi Pdf

Semigroups of Bounded Operators and Second-Order Elliptic and Parabolic Partial Differential Equations aims to propose a unified approach to elliptic and parabolic equations with bounded and smooth coefficients. The book will highlight the connections between these equations and the theory of semigroups of operators, while demonstrating how the theory of semigroups represents a powerful tool to analyze general parabolic equations. Features Useful for students and researchers as an introduction to the field of partial differential equations of elliptic and parabolic types Introduces the reader to the theory of operator semigroups as a tool for the analysis of partial differential equations

Fifteen papers on differential equations

N. V. Azbelev
Fifteen papers on differential equations Book PDF

Author : N. V. Azbelev
Publisher : American Mathematical Soc.
Page : 300 pages
File Size : 54,6 Mb
Release : 1964-12-31
Category : Differential equations
ISBN : 0821896210

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Fifteen papers on differential equations by N. V. Azbelev Pdf

Lectures on Elliptic and Parabolic Equations in Hölder Spaces

Nikolaĭ Vladimirovich Krylov
Lectures on Elliptic and Parabolic Equations in H lder Spaces Book PDF

Author : Nikolaĭ Vladimirovich Krylov
Publisher : American Mathematical Soc.
Page : 164 pages
File Size : 41,8 Mb
Release : 1996
Category : Mathematics
ISBN : 9780821805695

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Lectures on Elliptic and Parabolic Equations in Hölder Spaces by Nikolaĭ Vladimirovich Krylov Pdf

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.

Elliptic, Hyperbolic and Mixed Complex Equations with Parabolic Degeneracy

Guo Chun Wen
Elliptic Hyperbolic and Mixed Complex Equations with Parabolic Degeneracy Book PDF

Author : Guo Chun Wen
Publisher : World Scientific
Page : 453 pages
File Size : 54,8 Mb
Release : 2008
Category : Mathematics
ISBN : 9789812779434

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Elliptic, Hyperbolic and Mixed Complex Equations with Parabolic Degeneracy by Guo Chun Wen Pdf

In the recent half-century, many mathematicians have investigated various problems on several equations of mixed type and obtained interesting results, with important applications to gas dynamics. However, the Tricomi problem of general mixed type equations of second order with parabolic degeneracy has not been completely solved, particularly the Tricomi and Frankl problems for general Chaplygin equation in multiply connected domains posed by L Bers, and the existence, regularity of solutions of the above problems for mixed equations with non-smooth degenerate curve in several domains posed by J M Rassias. The method revealed in this book is unlike any other, in which the hyperbolic number and hyperbolic complex function in hyperbolic domains, and the complex number and complex function in elliptic domains are used. The corresponding problems for first order complex equations with singular coefficients are first discussed, and then the problems for second order complex equations are considered, where we pose the new partial derivative notations and complex analytic methods such that the forms of the above first order complex equations in hyperbolic and elliptic domains are wholly identical. In the meantime, the estimates of solutions for the above problems are obtained, hence many open problems including the above TricomiOCo Bers and TricomiOCoFranklOCoRassias problems can be solved. Sample Chapter(s). Chapter 1: Elliptic Complex Equations of First Order (247 KB). Contents: Elliptic Complex Equations of First Order; Elliptic Complex Equations of Second Order; Hyperbolic Complex Equations of First and Second Orders; First Order Complex Equations of Mixed Type; Second Order Linear Equations of Mixed Type; Second Order Quasilinear Equations of Mixed Type. Readership: Graduate students and academics in analysis, differential equations and applied mathematics.

Lectures on Elliptic and Parabolic Equations in Sobolev Spaces

Nikolaĭ Vladimirovich Krylov
Lectures on Elliptic and Parabolic Equations in Sobolev Spaces Book PDF

Author : Nikolaĭ Vladimirovich Krylov
Publisher : American Mathematical Soc.
Page : 377 pages
File Size : 55,8 Mb
Release : 2008
Category : Differential equations, Elliptic
ISBN : 9780821846841

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Lectures on Elliptic and Parabolic Equations in Sobolev Spaces by Nikolaĭ Vladimirovich Krylov Pdf

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.

Elliptic and Parabolic Equations Involving the Hardy-Leray Potential

Ireneo Peral Alonso,Fernando Soria de Diego
Elliptic and Parabolic Equations Involving the Hardy Leray Potential Book PDF

Author : Ireneo Peral Alonso,Fernando Soria de Diego
Publisher : Walter de Gruyter GmbH & Co KG
Page : 514 pages
File Size : 41,8 Mb
Release : 2021-02-22
Category : Mathematics
ISBN : 9783110606270

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Elliptic and Parabolic Equations Involving the Hardy-Leray Potential by Ireneo Peral Alonso,Fernando Soria de Diego Pdf

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.

Nonlinear Parabolic and Elliptic Equations

C.V. Pao
Nonlinear Parabolic and Elliptic Equations Book PDF

Author : C.V. Pao
Publisher : Springer Science & Business Media
Page : 786 pages
File Size : 50,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461530343

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Nonlinear Parabolic and Elliptic Equations by C.V. Pao Pdf

In response to the growing use of reaction diffusion problems in many fields, this monograph gives a systematic treatment of a class of nonlinear parabolic and elliptic differential equations and their applications these problems. It is an important reference for mathematicians and engineers, as well as a practical text for graduate students.

Elliptic and Parabolic Problems

C Bandle,Michel Chipot,Josef Bemelmans,J Saint Jean Paulin,I Shafrir
Elliptic and Parabolic Problems Book PDF

Author : C Bandle,Michel Chipot,Josef Bemelmans,J Saint Jean Paulin,I Shafrir
Publisher : CRC Press
Page : 272 pages
File Size : 41,5 Mb
Release : 2020-11-26
Category : Mathematics
ISBN : 9781000115277

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Elliptic and Parabolic Problems by C Bandle,Michel Chipot,Josef Bemelmans,J Saint Jean Paulin,I Shafrir Pdf

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. -------------------------------------

Second-Order Equations With Nonnegative Characteristic Form

O. Oleinik
Second Order Equations With Nonnegative Characteristic Form Book PDF

Author : O. Oleinik
Publisher : Springer Science & Business Media
Page : 265 pages
File Size : 51,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468489651

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Second-Order Equations With Nonnegative Characteristic Form by O. Oleinik Pdf

Second order equations with nonnegative characteristic form constitute a new branch of the theory of partial differential equations, having arisen within the last 20 years, and having undergone a particularly intensive development in recent years. An equation of the form (1) is termed an equation of second order with nonnegative characteristic form on a set G, kj if at each point x belonging to G we have a (xHk~j ~ 0 for any vector ~ = (~l' ... '~m)' In equation (1) it is assumed that repeated indices are summed from 1 to m, and x = (x l' ••• , x ). Such equations are sometimes also called degenerating m elliptic equations or elliptic-parabolic equations. This class of equations includes those of elliptic and parabolic types, first order equations, ultraparabolic equations, the equations of Brownian motion, and others. The foundation of a general theory of second order equations with nonnegative characteristic form has now been established, and the purpose of this book is to pre sent this foundation. Special classes of equations of the form (1), not coinciding with the well-studied equations of elliptic or parabolic type, were investigated long ago, particularly in the paper of Picone [105], published some 60 years ago.