Symmetrization And Applications
Symmetrization And Applications

Author: S Kesavan

Publisher: World Scientific

Published: 2006-04-25

Total Pages: 162

ISBN-13: 9814478296

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The study of isoperimetric inequalities involves a fascinating interplay of analysis, geometry and the theory of partial differential equations. Several conjectures have been made and while many have been resolved, a large number still remain open.One of the principal tools in the study of isoperimetric problems, especially when spherical symmetry is involved, is Schwarz symmetrization, which is also known as the spherically symmetric and decreasing rearrangement of functions. The aim of this book is to give an introduction to the theory of Schwarz symmetrization and study some of its applications.The book gives an modern and up-to-date treatment of the subject and includes several new results proved recently. Effort has been made to keep the exposition as simple and self-contained as possible. A knowledge of the existence theory of weak solutions of elliptic partial differential equations in Sobolev spaces is, however, assumed. Apart from this and a general mathematical maturity at the graduate level, there are no other prerequisites.

Symmetrization & Applications
Symmetrization & Applications

Author: S. Kesavan

Publisher: World Scientific

Published: 2006

Total Pages: 164

ISBN-13: 9812773932

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The study of isoperimetric inequalities involves a fascinating interplay of analysis, geometry and the theory of partial differential equations. Several conjectures have been made and while many have been resolved, a large number still remain open.One of the principal tools in the study of isoperimetric problems, especially when spherical symmetry is involved, is Schwarz symmetrization, which is also known as the spherically symmetric and decreasing rearrangement of functions. The aim of this book is to give an introduction to the theory of Schwarz symmetrization and study some of its applications.The book gives an modern and up-to-date treatment of the subject and includes several new results proved recently. Effort has been made to keep the exposition as simple and self-contained as possible. A knowledge of the existence theory of weak solutions of elliptic partial differential equations in Sobolev spaces is, however, assumed. Apart from this and a general mathematical maturity at the graduate level, there are no other prerequisites.

Symmetrization in Analysis
Symmetrization in Analysis

Author: Albert Baernstein II

Publisher: Cambridge University Press

Published: 2019-03-14

Total Pages: 493

ISBN-13: 0521830478

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Develops the modern theory of symmetrization including applications to geometry, PDEs, and real and complex analysis.

Symmetrization in Analysis
Symmetrization in Analysis

Author: Albert Baernstein II

Publisher: Cambridge University Press

Published: 2019-03-14

Total Pages: 493

ISBN-13: 1108583407

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Symmetrization is a rich area of mathematical analysis whose history reaches back to antiquity. This book presents many aspects of the theory, including symmetric decreasing rearrangement and circular and Steiner symmetrization in Euclidean spaces, spheres and hyperbolic spaces. Many energies, frequencies, capacities, eigenvalues, perimeters and function norms are shown to either decrease or increase under symmetrization. The book begins by focusing on Euclidean space, building up from two-point polarization with respect to hyperplanes. Background material in geometric measure theory and analysis is carefully developed, yielding self-contained proofs of all the major theorems. This leads to the analysis of functions defined on spheres and hyperbolic spaces, and then to convolutions, multiple integrals and hypercontractivity of the Poisson semigroup. The author's 'star function' method, which preserves subharmonicity, is developed with applications to semilinear PDEs. The book concludes with a thorough self-contained account of the star function's role in complex analysis, covering value distribution theory, conformal mapping and the hyperbolic metric.

Similarity Search and Applications
Similarity Search and Applications

Author: Giuseppe Amato

Publisher: Springer Nature

Published: 2019-09-24

Total Pages: 372

ISBN-13: 3030320472

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This book constitutes the refereed proceedings of the 12th International Conference on Similarity Search and Applications, SISAP 2019, held in Newark, NJ, USA, in October 2019. The 12 full papers presented together with 18 short and 3 doctoral symposium papers were carefully reviewed and selected from 42 submissions. The papers are organized in topical sections named: Similarity Search and Retrieval; The Curse of Dimensionality; Clustering and Outlier Detection; Subspaces and Embeddings; Applications; Doctoral Symposium Papers.

High-Dimensional Probability
High-Dimensional Probability

Author: Roman Vershynin

Publisher: Cambridge University Press

Published: 2018-09-27

Total Pages: 299

ISBN-13: 1108415199

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An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.

Rewriting Techniques and Applications
Rewriting Techniques and Applications

Author: Leo Bachmair

Publisher: Springer Science & Business Media

Published: 2000-06-28

Total Pages: 284

ISBN-13: 354067778X

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This book constitutes the refereed proceedings of the 11th International Conference on Rewriting Techniques and Applications, RTA 2000, held in Norwich, UK, in July 2000. The 15 revised full papers and three system descriptions presented together with two invited contributions were carefully reviewed and selected from 44 submissions. All current aspects of rewriting are addressed.