Lectures On Elliptic And Parabolic Equations In H Lder Spaces
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Lectures on Elliptic and Parabolic Equations in H lder Spaces
Author | : Nikolaĭ Vladimirovich Krylov |
Publsiher | : American Mathematical Soc. |
Total Pages | : 164 |
Release | : 1996 |
Genre | : Mathematics |
ISBN | : 9780821805695 |
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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.
Lectures on Elliptic and Parabolic Equations in H lder Spaces
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Author | : Nikolaĭ Vladimirovich Krylov |
Publsiher | : Unknown |
Total Pages | : 166 |
Release | : 1900 |
Genre | : Differential equations, Elliptic |
ISBN | : 1470420708 |
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Lectures on Elliptic and Parabolic Equations in Sobolev Spaces
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Author | : Nikolaĭ Vladimirovich Krylov |
Publsiher | : Unknown |
Total Pages | : 377 |
Release | : 1900 |
Genre | : Differential equations, Elliptic |
ISBN | : 1470421216 |
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Lectures on Elliptic and Parabolic Equations in Sobolev Spaces
Author | : Nikolaĭ Vladimirovich Krylov |
Publsiher | : American Mathematical Soc. |
Total Pages | : 377 |
Release | : 2008 |
Genre | : Mathematics |
ISBN | : 9780821846841 |
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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
Author | : Zhuoqun Wu,Jingxue Yin,Chunpeng Wang |
Publsiher | : World Scientific Publishing Company |
Total Pages | : 425 |
Release | : 2006-10-17 |
Genre | : Mathematics |
ISBN | : 9789813101708 |
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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.
Quasilinear Degenerate and Nonuniformly Elliptic and Parabolic Equations of Second Order
Author | : A. V. Ivanov |
Publsiher | : American Mathematical Soc. |
Total Pages | : 306 |
Release | : 1984 |
Genre | : Mathematics |
ISBN | : 0821830805 |
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Elements of Combinatorial and Differential Topology
Author | : V. V. Prasolov |
Publsiher | : American Mathematical Society |
Total Pages | : 331 |
Release | : 2022-03-25 |
Genre | : Mathematics |
ISBN | : 9781470469443 |
Download Elements of Combinatorial and Differential Topology Book in PDF, Epub and Kindle
Modern topology uses very diverse methods. This book is devoted largely to methods of combinatorial topology, which reduce the study of topological spaces to investigations of their partitions into elementary sets, and to methods of differential topology, which deal with smooth manifolds and smooth maps. Many topological problems can be solved by using either of these two kinds of methods, combinatorial or differential. In such cases, both approaches are discussed. One of the main goals of this book is to advance as far as possible in the study of the properties of topological spaces (especially manifolds) without employing complicated techniques. This distinguishes it from the majority of other books on topology. The book contains many problems; almost all of them are supplied with hints or complete solutions.
Linear and Quasi linear Equations of Parabolic Type
Author | : Olʹga A. Ladyženskaja,Vsevolod Alekseevich Solonnikov |
Publsiher | : American Mathematical Soc. |
Total Pages | : 74 |
Release | : 1988 |
Genre | : Mathematics |
ISBN | : 0821815733 |
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Equations of parabolic type are encountered in many areas of mathematics and mathematical physics, and those encountered most frequently are linear and quasi-linear parabolic equations of the second order. In this volume, boundary value problems for such equations are studied from two points of view: solvability, unique or otherwise, and the effect of smoothness properties of the functions entering the initial and boundary conditions on the smoothness of the solutions.