论文信息 - On the cases of equality in Bobkov's inequality and Gaussian rearrangement

On the cases of equality in Bobkov's inequality and Gaussian rearrangement

Abstract. We determine all of the cases of equality in a recent inequality of Bobkov that implies the isoperimetric inequality on Gauss space. As an application we determine all of the cases of equality in the Gauss space analog of the Faber-Krahn inequality.

E. Carlen | E. A. Carlen | C. Kerce | C. Kerce

[1] William P. Ziemer,et al. Minimal rearrangements of Sobolev functions. , 1987 .

[2] A. Ehrhard. Inégalités isopérimétriques et intégrales de Dirichlet gaussiennes , 1984 .

[3] S. Bobkov. An isoperimetric inequality on the discrete cube, and an elementary proof of the isoperimetric inequality in Gauss space , 1997 .

[4] Elliott H. Lieb,et al. Symmetric decreasing rearrangement is sometimes continuous , 1989 .

[5] M. Ledoux,et al. Lévy–Gromov’s isoperimetric inequality for an infinite dimensional diffusion generator , 1996 .

[6] L. Evans. Measure theory and fine properties of functions , 1992 .

[7] F. G. Mehler. Ueber die Entwicklung einer Function von beliebig vielen Variablen nach Laplaceschen Functionen höherer Ordnung. , 1866 .

[8] G. Pólya,et al. Isoperimetric inequalities in mathematical physics , 1951 .

[9] E. Krahn,et al. Über eine von Rayleigh formulierte Minimaleigenschaft des Kreises , 1925 .

[10] W. Ziemer. Weakly Differentiable Functions: Sobolev Spaces and Functions of Bounded Variation , 1989 .

[11] M. Ledoux. A Short Proof of the Gaussian Isoperimetric Inequality , 1998 .