Book contents
- Frontmatter
- Contents
- Notation
- Foreword
- Preface
- Introduction
- 1 Rearrangements
- 2 Main Inequalities on Rn3
- 3 Dirichlet Integral Inequalities
- 4 Geometric Isoperimetric and Sharp Sobolev Inequalities
- 5 Isoperimetric Inequalities for Physical Quantities
- 6 Steiner Symmetrization
- 7 Symmetrization on Spheres, and Hyperbolic and Gauss Spaces
- 8 Convolution and Beyond
- 9 The ⋆-Function
- 10 Comparison Principles for Semilinear Poisson PDEs
- 11 The ⋆-Function in Complex Analysis
- References
- Index
1 - Rearrangements
Published online by Cambridge University Press: 22 February 2019
Book contents
- Frontmatter
- Contents
- Notation
- Foreword
- Preface
- Introduction
- 1 Rearrangements
- 2 Main Inequalities on Rn3
- 3 Dirichlet Integral Inequalities
- 4 Geometric Isoperimetric and Sharp Sobolev Inequalities
- 5 Isoperimetric Inequalities for Physical Quantities
- 6 Steiner Symmetrization
- 7 Symmetrization on Spheres, and Hyperbolic and Gauss Spaces
- 8 Convolution and Beyond
- 9 The ⋆-Function
- 10 Comparison Principles for Semilinear Poisson PDEs
- 11 The ⋆-Function in Complex Analysis
- References
- Index
Summary
This chapter presents the basic theory of rearrangements of functions, with special emphasis on the symmetric decreasing rearrangement. Another type of rearrangement central to thisbook ispolarization with respect to an affinehyperplane. Examples and graphs are included throught the chapter.
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- Symmetrization in Analysis , pp. 16 - 53Publisher: Cambridge University PressPrint publication year: 2019
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