Theory of Sobolev Multipliers
Theory of Sobolev Multipliers

Author: Vladimir Maz'ya

Publisher: Springer Science & Business Media

Published: 2008-10-13

Total Pages: 615

ISBN-13: 3540694927

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The first part of this book offers a comprehensive overview of the theory of pointwise multipliers acting in pairs of spaces of differentiable functions. The second part of the book explores several applications of this theory.

Theory and Applications of Differentiable Functions of Several Variables
Theory and Applications of Differentiable Functions of Several Variables

Author:

Publisher: American Mathematical Soc.

Published: 1994

Total Pages: 276

ISBN-13: 9780821802762

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This book explores various topical trends in the theory of differentiable functions of several real variables and its applications. Among the subjects covered are: imbedding of various spaces of differentiable functions defined on sets in Euclidean space, on a sphere, and in a polydisc; approximation of functions; estimates for the norms of various integral operators in weighted space; conditions for stabilization of a function to a polynomial; sufficient conditions for multipliers; construction of unconditional bases in anisotropic spaces; existence of entire solutions for quasilinear equations; and establishment of an asymptotic formula for the kernels of powers of the resolvent of elliptic operators.

Function Spaces, Differential Operators and Nonlinear Analysis
Function Spaces, Differential Operators and Nonlinear Analysis

Author: Dorothee Haroske

Publisher: Birkhäuser

Published: 2012-12-06

Total Pages: 462

ISBN-13: 3034880359

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This volume is dedicated to our teacher and friend Hans Triebel. The core of the book is based on lectures given at the International Conference "Function Spaces, Differential Operators and Nonlinear Analysis" (FSDONA--01) held in Teistungen, Thuringia / Germany, from June 28 to July 4,2001, in honour of his 65th birthday. This was the fifth in a series of meetings organised under the same name by scientists from Finland (Helsinki, Oulu) , the Czech Republic (Prague, Plzen) and Germany (Jena) promoting the collaboration of specialists in East and West, working in these fields. This conference was a very special event because it celebrated Hans Triebel's extraordinary impact on mathematical analysis. The development of the mod ern theory of function spaces in the last 30 years and its application to various branches in both pure and applied mathematics is deeply influenced by his lasting contributions. In a series of books Hans Triebel has given systematic treatments of the theory of function spaces from different points of view, thus revealing its interdependence with interpolation theory, harmonic analysis, partial differential equations, nonlinear operators, entropy, spectral theory and, most recently, anal ysis on fractals. The presented collection of papers is a tribute to Hans Triebel's distinguished work. The book is subdivided into three parts: • Part I contains the two invited lectures by O.V. Besov (Moscow) and D.E. Edmunds (Sussex) having a survey character and honouring Hans Triebel's contributions.

Differentiable Functions On Bad Domains
Differentiable Functions On Bad Domains

Author: Vladimir G Maz'ya

Publisher: World Scientific

Published: 1998-01-15

Total Pages: 502

ISBN-13: 9814498564

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The spaces of functions with derivatives in Lp, called the Sobolev spaces, play an important role in modern analysis. During the last decades, these spaces have been intensively studied and by now many problems associated with them have been solved. However, the theory of these function classes for domains with nonsmooth boundaries is still in an unsatisfactory state.In this book, which partially fills this gap, certain aspects of the theory of Sobolev spaces for domains with singularities are studied. We mainly focus on the so-called imbedding theorems, extension theorems and trace theorems that have numerous applications to partial differential equations. Some of such applications are given.Much attention is also paid to counter examples showing, in particular, the difference between Sobolev spaces of the first and higher orders. A considerable part of the monograph is devoted to Sobolev classes for parameter dependent domains and domains with cusps, which are the simplest non-Lipschitz domains frequently used in applications.This book will be interesting not only to specialists in analysis but also to postgraduate students.

Harmonic Analysis and Partial Differential Equations
Harmonic Analysis and Partial Differential Equations

Author: Anatoly Golberg

Publisher: Springer Nature

Published: 2023-04-26

Total Pages: 319

ISBN-13: 3031254244

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Over the course of his distinguished career, Vladimir Maz'ya has made a number of groundbreaking contributions to numerous areas of mathematics, including partial differential equations, function theory, and harmonic analysis. The chapters in this volume - compiled on the occasion of his 80th birthday - are written by distinguished mathematicians and pay tribute to his many significant and lasting achievements.

Differential Equations and Numerical Mathematics
Differential Equations and Numerical Mathematics

Author: G. I. Marchuk

Publisher: Elsevier

Published: 2014-06-25

Total Pages: 165

ISBN-13: 1483154548

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Differential Equations and Numerical Mathematics contains selected papers presented in a national conference held in Novosibirsk on September 1978. This book, as the conference, is organized into three sections. Section A describes the modern theory of efficient cubature formulas; embedding theorems; and problems of spectral analysis. Section B considers the theoretical questions of partial differential equations, with emphasis on hyperbolic equations and systems, formulations, and methods for nonclassical problems of mathematical physics. Section C addresses the various problems of numerical mathematics, with focus on the optimum and asymptotically optimum algorithms for solving the problems of numerical mathematics.

Morrey Spaces
Morrey Spaces

Author: David Adams

Publisher: Birkhäuser

Published: 2015-12-31

Total Pages: 133

ISBN-13: 3319266810

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In this set of lecture notes, the author includes some of the latest research on the theory of Morrey Spaces associated with Harmonic Analysis. There are three main claims concerning these spaces that are covered: determining the integrability classes of the trace of Riesz potentials of an arbitrary Morrey function; determining the dimensions of singular sets of weak solutions of PDE (e.g. The Meyers-Elcart System); and determining whether there are any “full” interpolation results for linear operators between Morrey spaces. This book will serve as a useful reference to graduate students and researchers interested in Potential Theory, Harmonic Analysis, PDE, and/or Morrey Space Theory.