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.
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Well-suited for a special topics course at the graduate level. -- Mathematical Reviews
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symmetrized problem, classical isoperimetric inequality, first positive zero, decreasing rearrangement, first eigenfunction, warping function, electrostatic capacity, principal eigenvalue, isoperimetric inequalities, variational characterization, first eigenvalue, plane domains, geometric measure theory, torsional rigidity, equality case, bounded domain Key Phrases - Capitalized Phrases (CAPs): (learn more)
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symmetrized problem, classical isoperimetric inequality, first positive zero, decreasing rearrangement, first eigenfunction, warping function, electrostatic capacity, principal eigenvalue, isoperimetric inequalities, variational characterization, first eigenvalue, plane domains, geometric measure theory, torsional rigidity, equality case, bounded domain Key Phrases - Capitalized Phrases (CAPs): (learn more)
Saint Venant, Lord Rayleigh New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 5
books:
- Methods of Mathematical Physics, Vol. 1 by Richard Courant in Back Matter
- Topics in Functional Analysis and Applications by S. Kesavan in Back Matter
- Isoperimetric Inequalities (Monograph & Studies in Mathematics) by Catherine Bandle in Back Matter
- Geometric Measure Theory (Classics in Mathematics) by Herbert Federer in Back Matter
- Sobolev spaces, Volume 65 (Pure and Applied Mathematics) by Author Unknown in Back Matter
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