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# memo_has_moved_text(); Some connections between isoperimetric and Sobolev-type inequalities

Serguei G. Bobkov and Christian Houdré

Publication: Memoirs of the American Mathematical Society
Publication Year 1997: Volume 129, Number 616
ISBNs: 978-0-8218-0642-5 (print); 978-1-4704-0201-3 (online)
DOI: http://dx.doi.org/10.1090/memo/0616
MathSciNet review: 1396954
MSC (1991): Primary 46E35; Secondary 49Q20, 60E15

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Chapters

• 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 $\mathbf {R}^n$