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Develops the modern theory of symmetrization including applications to geometry, PDEs, and real and complex analysis.
List of contents
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.
About the author
Albert Baernstein, II was Professor in the Department of Mathematics at Washington University, St Louis before his death in 2014. He gained international renown for innovative solutions to extremal problems in complex and harmonic analysis. His invention of the 'star function' method in the 1970s prompted an invitation to the International Congress of Mathematicians held in Helsinki in 1978, and during the 1980s and 90s he substantially extended the breadth and applications of this method.
Summary
Many extremal problems in mathematics and physics have symmetric solutions whose analytic and geometric properties often have elegant formulations. This book develops and applies symmetrization techniques in geometry, PDEs, and real and complex analysis. It will be a valuable reference, with self-contained treatments of all the major theorems.
