Sobolev Spaces in Mathematics III: Applications in Mathematical Physics / Edition 1

Sobolev Spaces in Mathematics III: Applications in Mathematical Physics / Edition 1

by Victor Isakov
     
 

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ISBN-10: 144192759X

ISBN-13: 9781441927590

Pub. Date: 11/19/2010

Publisher: Springer New York

The mathematical works of S.L. Sobolev were strongly motivated by particular problems coming from applications. In his celebrated book Applications of Functional Analysis in Mathematical Physics (1950) and other works, S. Sobolev introduced general methods that turned out to be very influential in the study of mathematical physics in the second half of the XXth

Overview

The mathematical works of S.L. Sobolev were strongly motivated by particular problems coming from applications. In his celebrated book Applications of Functional Analysis in Mathematical Physics (1950) and other works, S. Sobolev introduced general methods that turned out to be very influential in the study of mathematical physics in the second half of the XXth century. This volume, dedicated to the centenary of S.L. Sobolev, presents the latest results on some important problems of mathematical physics describing, in particular, phenomena of superconductivity with random fluctuations, wave propagation, perforated domains and bodies with defects of different types, spectral asymptotics for Dirac energy, Lame system with residual stress, optimal control problems for partial differential equations and inverse problems admitting numerous interpretations. Methods of modern functional analysis are essentially used in the investigation of these problems.

Product Details

ISBN-13:
9781441927590
Publisher:
Springer New York
Publication date:
11/19/2010
Series:
International Mathematical Series, #10
Edition description:
Softcover reprint of hardcover 1st ed. 2009
Pages:
336
Product dimensions:
6.14(w) x 9.21(h) x 0.77(d)

Table of Contents

I. Sobolev Type Inequalities Vladimir Maz'ya Ed.

My Love Affair with the Sobolev Inequality David R. Adams 1

Maximal Functions in Sobolev Spaces Daniel Aalto Juha Kinnunen 25

Hardy Type Inequalities Via Riccati and Sturm-Liouville Equations Sergey Bobkov Friedrich Gotze 69

Quantitative Sobolev and Hardy Inequalities, and Related Symmetrization Principles Andrea Cianchi 87

Inequalities of Hardy-Sobolev Type in Carnot-Caratheodory Spaces Donatella Danielli Nicola Garofalo Nguyen Cong Phuc 117

Sobolev Embeddings and Hardy Operators David E. Edmunds W. Desmond Evans 153

Sobolev Mappings between Manifolds and Metric Spaces Piotr Hajlasz 185

A Collection of Sharp Dilation Invariant Integral Inequalities for Differentiable Functions Vladimir Maz'ya Tatyana Shaposhnikova 223

Optimality of Function Spaces in Sobolev Embeddings Lubos Pick 249

On the Hardy-Sobolev-Maz'ya Inequality and Its Generalizations Yehuda Pinchover Kyril Tintarev 281

Sobolev Inequalities in Familiar and Unfamiliar Settings Laurent Saloff-Coste 299

A Universality Property of Sobolev Spaces in Metric Measure Spaces Nageswari Shanmugalingam 345

Cocompact Imbeddings and Structure of Weakly Convergent Sequences Kiril Tintarev 361

Index 377

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