Symmetrization and Applications.
Başlık:
Symmetrization and Applications.
Yazar:
Kesavan, S.
ISBN:
9789812773937
Yazar Ek Girişi:
Fiziksel Tanımlama:
1 online resource (162 pages)
Seri:
Series in Analysis ; v.3
Series in Analysis
İçerik:
Contents -- Preface -- Notations -- 1. Symmetrization -- 1.1 The Decreasing Rearrangement -- 1.2 Some Rearrangement Inequalities -- 1.3 Schwarz Symmetrization -- 1.4 Variations on the Theme -- 2. Some Classical Inequalities -- 2.1 The Isoperimetric Inequality -- 2.2 The Co-area Formula -- 2.3 The Polya - Szego Theorem -- 2.4 Sobolev's Inequality -- 3. Comparison Theorems -- 3.1 Talenti's Theorem -- 3.2 The Equality Case -- 3.3 Sobolev Imbeddings -- 3.4 The Obstacle Problem -- 3.5 Electrostatic Capacity -- 3.6 The Saint Venant Problem -- 3.7 Comments -- 4. Eigenvalue Problems -- 4.1 The Faber - Krahn Inequality -- 4.2 The Szego - Weinberger Inequality -- 4.3 Chiti's Theorem -- 4.4 The Payne - Polya - Weinberger Conjecture -- 4.5 Rayleigh's Conjecture for Clamped Plates -- 4.6 The Buckling Problem -- 4.7 Comments -- 5. Nonlinear Problems -- 5.1 Payne - Rayner Type Inequalities -- 5.2 A System of Semilinear Equations -- 5.3 Comments -- Bibliography -- Index.
Özet:
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.
Notlar:
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2017. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
Tür:
Elektronik Erişim:
Click to View