Symmetrization in Analysis

ISBN-13: 9780521830478 / Angielski / Twarda / 2019 / 490 str.

Albert Baernstein II

Opis

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

Recenzje

'The book itself is a comprehensive and detailed study of the notion of symmetrization and is a welcome addition to existing literature on the subject. This book is a remarkable text collecting a variety of ideas in one unified framework; historical notes put the results in perspective. This book is very well written and will be useful to people working in a wide variety of fields.' Stefan Steinerberger, MathsSciNet

Spis treści

Foreword Walter Hayman; Preface David Drasin and Richard S. Laugesen; Introduction; 1. Rearrangements; 2. Main inequalities on Rn; 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.