Some connections between isoperimetric and Sobolev-type inequalities

Some connections between isoperimetric and Sobolev-type inequalities / Serguei G. Bobkov, Christian Houdré.

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Bibliographic Details
Main Author: Bobkov, Serguei G. (Serguei Germanovich), 1961-
Other Authors: Houdré, Christian
Format: eBook
Language:English
Published: Providence, R.I. : American Mathematical Society, ©1997.
Series:Memoirs of the American Mathematical Society ; no. 616.
Subjects:
Sobolov spaces.
Geometric measure theory.
Uniform distribution (Probability theory)
Gaussian processes.
LITERARY CRITICISM > American > General.
Gaussian processes
Geometric measure theory
Online Access:Click for online access
Table of Contents:
  • 1. Introduction 2. Differential and integral forms of isoperimetric inequalities 3. Proof of Theorem 1.1 4. A relation between the distribution of a function and its derivative 5. A variational problem 6. The discrete version of Theorem 5.1 7. Proof of Propositions 1.3 and 1.5 8. A special case of Theorem 1.2 9. The uniform distribution on the sphere 10. Existence of optimal Orlicz spaces 11. Proof of Theorem 1.9 (the case of the sphere) 12. Proof of Theorem 1.9 (the Gaussian case) 13. The isoperimetric problem on the real line 14. Isoperimetric and Sobolev-type inequalities on the real line 15. Extensions of Sobolev-type inequalities to product measures on $\mathbf {R}^n$

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