عنوان

Symmetrization in analysis /

(Number (ISBN

1108615112

(Number (ISBN

1139020242

(Number (ISBN

9781108615112

(Number (ISBN

9781139020244

Erroneous ISBN

9780521830478

Title Proper

Symmetrization in analysis /

General Material Designation

[Book]

First Statement of Responsibility

Albert Baernstein II ; with David Drasin, Richard Laugesen.

Place of Publication, Distribution, etc.

Cambridge :

Name of Publisher, Distributor, etc.

Cambridge University Press,

Date of Publication, Distribution, etc.

[2019]

Date of Publication, Distribution, etc.

©2019

Specific Material Designation and Extent of Item

1 online resource (xviii, 473 pages)

Series Title

New mathematical monographs ;

Volume Designation

36

Text of Note

Includes bibliographical references and index.

Text of Note

Cover; Half-title; Series information; Title page; Copyright information; Contents; Notation; Foreword; Preface; Introduction; 1 Rearrangements; 1.1 The Distribution Function; 1.2 The Decreasing Rearrangement; 1.3 Induced Measures; 1.4 Measure Preserving Transformations; 1.5 Nonatomic Measure Spaces; 1.6 Symmetric Decreasing Rearrangement on R[sup(n)]; 1.7 Polarization on R[sup(n)]; 1.8 Convergence Theorems for Rearrangements; 1.9 Notes and Comments; 2 Main Inequalities on R[sup(n)]; 2.1 Convex and AL Functions; 2.2 Main Inequalities for Two-Point Symmetrization

Text of Note

3.4 Sobolev Spaces W[sup(1,p)](R[sup(n)])3.5 Weak Compactness; 3.6 Symmetrization Decreases the p-Dirichlet Integral in W[sup(1,p)](R[sup(n)]); 3.7 Continuity and Discontinuity of the Symmetric Decreasing Rearrangement Operator; 3.8 Notes and Comments; 4 Geometric Isoperimetric and Sharp Sobolev Inequalities; 4.1 Hausdorff Measures, Area Formula, and the Gauss-Green Theorem; 4.2 Functions of Bounded Variation in R[sup(n)]; 4.3 Isoperimetric Inequalities for Perimeter and Hausdorff Measure; 4.4 Isoperimetric Inequalities for Minkowski Content; 4.5 Coarea Formula

Text of Note

5.8 Notes and Comments6 Steiner Symmetrization; 6.1 Definition of Steiner Symmetrization; 6.2 Steiner Counterparts for Results in Chapter 1; 6.3 Steiner Analogues for Two Simple Polarization Results; 6.4 Certain Integral Functionals Increase or Decrease under Steiner Symmetrization; 6.5 Steiner Symmetrization Decreases the Modulus of Continuity; 6.6 Steiner Symmetrization Decreases Dirichlet Integrals; 6.7 Proof of Lemma 6.18; 6.8 Steiner Symmetrization Decreases p-Dirichlet Integrals in W[sup(1,p)](R[sup(n)]); 6.9 Steiner Symmetrization Decreases Surface Area

0

8

8

Text of Note

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.

Title

Symmetrization in analysis.

International Standard Book Number

9780521830478

Control theory.

Integral equations.

Mathematical analysis.

Symmetric functions.

Control theory.

Integral equations.

Mathematical analysis.

MATHEMATICS-- Calculus.

MATHEMATICS-- Mathematical Analysis.

Symmetric functions.

MAT-- 005000

MAT-- 034000

Number

Edition

Class number

Book number

Baernstein, Albert,II,1941-2014

Drasin, D., (David),1940-

Laugesen, Richard,1967-

Date of Transaction

20200822120325.0

Cataloguing Rules (Descriptive Conventions))

pn

Electronic name

[Book]

Y