Some connections between isoperimetric and Sobolev-type inequalities / [electronic resource] Serguei G. Bobkov, Christian Houdr�e.

By: Bobkov, Serguei G. (Serguei Germanovich), 1961-Contributor(s): Houdr�e, ChristianMaterial type: TextTextSeries: Memoirs of the American Mathematical Society ; v. 616Publication details: Providence, R.I. : American Mathematical Society, c1997Description: 1 online resource (viii, 111 p. : ill.)ISBN: 9781470402013 (online)Subject(s): Sobolov spaces | Geometric measure theory | Uniform distribution (Probability theory) | Gaussian processesAdditional physical formats: Some connections between isoperimetric and Sobolev-type inequalities /DDC classification: 813/.54 | 510 s | 515/.73 LOC classification: QA3 | .A57 no. 616 | QA323Online resources: Contents | Contents
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 $\mathbf {R}^n$
Item type: E-BOOKS
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Link to resource Available EBK13069

"September 1997, volume 129, number 616 (end of volume)."

Includes bibliographical references (p. 109-111).

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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Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2012

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