Nonlinear Potential Theory and Weighted Sobolev Spaces PDF Download

Author: Bengt O. Turesson
Publisher: Springer
ISBN: 3540451684
Category : Mathematics
Languages : en
Pages : 188

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Book Description
The book systematically develops the nonlinear potential theory connected with the weighted Sobolev spaces, where the weight usually belongs to Muckenhoupt's class of Ap weights. These spaces occur as solutions spaces for degenerate elliptic partial differential equations. The Sobolev space theory covers results concerning approximation, extension, and interpolation, Sobolev and Poincaré inequalities, Maz'ya type embedding theorems, and isoperimetric inequalities. In the chapter devoted to potential theory, several weighted capacities are investigated. Moreover, "Kellogg lemmas" are established for various concepts of thinness. Applications of potential theory to weighted Sobolev spaces include quasi continuity of Sobolev functions, Poincaré inequalities, and spectral synthesis theorems.

Author: Bengt Ove Turesson
Publisher:
ISBN: 9789178715497
Category : Nonlinear theories
Languages : en
Pages : 171

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Book Description

Author: Juha Heinonen
Publisher: Courier Dover Publications
ISBN: 048682425X
Category : Mathematics
Languages : en
Pages : 417

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Book Description
A self-contained treatment appropriate for advanced undergraduate and graduate students, this volume offers a detailed development of the necessary background for its survey of the nonlinear potential theory of superharmonic functions. Starting with the theory of weighted Sobolev spaces, the text advances to the theory of weighted variational capacity. Succeeding chapters investigate solutions and supersolutions of equations, with emphasis on refined Sobolev spaces, variational integrals, and harmonic functions. Chapter 7 defines superharmonic functions via the comparison principle, and chapters 8 through 14 form the core of the nonlinear potential theory of superharmonic functions. Topics include balayage; Perron's method, barriers, and resolutivity; polar sets; harmonic measure; fine topology; harmonic morphisms; and quasiregular mappings. The book concludes with explorations of axiomatic nonlinear potential theory and helpful appendixes.

Author: Juha Heinonen
Publisher: Courier Dover Publications
ISBN: 0486830462
Category : Mathematics
Languages : en
Pages : 417

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Book Description
A self-contained treatment appropriate for advanced undergraduates and graduate students, this text offers a detailed development of the necessary background for its survey of the nonlinear potential theory of superharmonic functions. 1993 edition.

Author: Vladimir Maz'ya
Publisher: Springer Science & Business Media
ISBN: 038785648X
Category : Mathematics
Languages : en
Pages : 395

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Book Description
This volume mark’s the centenary of the birth of the outstanding mathematician of the 20th century, Sergey Sobolev. It includes new results on the latest topics of the theory of Sobolev spaces, partial differential equations, analysis and mathematical physics.

Author: Hitoshi Tanaka
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110726106
Category : Mathematics
Languages : en
Pages : 315

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Book Description
This monograph is devoted to harmonic analysis and potential theory. The authors study these essentials carefully and present recent researches based on the papers including by authors in an accessible manner for graduate students and researchers in pure and applied analysis.

Author: Vladimir Maz'ya
Publisher: Springer Science & Business Media
ISBN: 3642155642
Category : Mathematics
Languages : en
Pages : 882

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Book Description
Sobolev spaces play an outstanding role in modern analysis, in particular, in the theory of partial differential equations and its applications in mathematical physics. They form an indispensable tool in approximation theory, spectral theory, differential geometry etc. The theory of these spaces is of interest in itself being a beautiful domain of mathematics. The present volume includes basics on Sobolev spaces, approximation and extension theorems, embedding and compactness theorems, their relations with isoperimetric and isocapacitary inequalities, capacities with applications to spectral theory of elliptic differential operators as well as pointwise inequalities for derivatives. The selection of topics is mainly influenced by the author’s involvement in their study, a considerable part of the text is a report on his work in the field. Part of this volume first appeared in German as three booklets of Teubner-Texte zur Mathematik (1979, 1980). In the Springer volume “Sobolev Spaces”, published in English in 1985, the material was expanded and revised. The present 2nd edition is enhanced by many recent results and it includes new applications to linear and nonlinear partial differential equations. New historical comments, five new chapters and a significantly augmented list of references aim to create a broader and modern view of the area.

Author: Vitali D. Milman
Publisher: Springer
ISBN: 3540720537
Category : Mathematics
Languages : en
Pages : 330

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Book Description
This collection of original papers related to the Israeli GAFA seminar (on Geometric Aspects of Functional Analysis) during the years 2004-2005 reflects the general trends of the theory and are a source of inspiration for research. Most of the papers deal with different aspects of the Asymptotic Geometric Analysis, ranging from classical topics in the geometry of convex bodies to the study of sections or projections of convex bodies.

Author: Martin Rasmussen
Publisher: Springer
ISBN: 3540712259
Category : Mathematics
Languages : en
Pages : 222

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Book Description
Although, bifurcation theory of equations with autonomous and periodic time dependence is a major object of research in the study of dynamical systems since decades, the notion of a nonautonomous bifurcation is not yet established. In this book, two different approaches are developed which are based on special definitions of local attractivity and repulsivity. It is shown that these notions lead to nonautonomous Morse decompositions.

Author: J. Azema
Publisher: Springer Science & Business Media
ISBN: 9783540416593
Category : Mathematics
Languages : en
Pages : 444

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Book Description
Researchers and graduate students in the theory of stochastic processes will find in this 35th volume some thirty articles on martingale theory, martingales and finance, analytical inequalities and semigroups, stochastic differential equations, functionals of Brownian motion and of Lévy processes. Ledoux's article contains a self-contained introduction to the use of semigroups in spectral gaps and logarithmic Sobolev inequalities; the contribution by Emery and Schachermayer includes an exposition for probabilists of Vershik's theory of backward discrete filtrations.