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

@article{Carlen1999OnTC,
  title={On the cases of equality in Bobkov's inequality and Gaussian rearrangement},
  author={Eric A. Carlen and Clayton Kerce},
  journal={Calculus of Variations and Partial Differential Equations},
  year={1999},
  volume={13},
  pages={1-18}
}
  • E. Carlen, C. Kerce
  • Published 1999
  • Mathematics
  • Calculus of Variations and Partial Differential Equations
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. 
On the Existence of Extremals for Moser-Type Inequalities in Gauss Space
The existence of an extremal in an exponential Sobolev type inequality, with optimal constant, in Gauss space is established. A key step in the proof is an augmented version of the relevant
Moser inequalities in Gauss space
The sharp constants in a family of exponential Sobolev type inequalities in Gauss space are exhibited. They constitute the Gaussian analogues of the Moser inequality in the borderline case of the
On the Case of Equalities in Comparison Results for Elliptic Equations Related to Gauss Measure
In this paper, we deal with a Dirichlet problem for linear elliptic equations related to Gauss measure. For this problem, we study the converse of some inequalities proved by other authors, in the
Bobkov’s Inequality via Optimal Control Theory
We give the simple proof of Bobkov's inequality using the arguments of dynamical programming principle. As a byproduct of the method we obtain a characterization of optimizers.
Essential connectedness and the rigidity problem for Gaussian symmetrization
We provide a geometric characterization of rigidity of equality cases in Ehrhard's symmetrization inequality for Gaussian perimeter. This condition is formulated in terms of a new measure-theoretic
ON THE ISOPERIMETRIC DEFICIT IN GAUSS
We prove a sharp quantitative version of the isoperimetric inequality in the space Rn endowed with the Gaussian measure.
On the Case of Equalities in Comparison Results for Parabolic Equations Related to Gauss Measure
We deal with linear parabolic equations related to Gauss measure. Firstly, we study the case of equalities in some comparison results proved by other authors and show that equalities are achieved
Hardy type inequalities and Gaussian measure
In this paper we prove some improved Hardy type inequalities with respect to the Gaussian measure. We show that they are strictly related to the well-known Gross Logarithmic Sobolev inequality.
Sharp exponential inequalities for the Ornstein-Uhlenbeck operator
Rigidity of some functional inequalities on RCD spaces
...
...

References

SHOWING 1-10 OF 16 REFERENCES
An isoperimetric inequality on the discrete cube, and an elementary proof of the isoperimetric inequality in Gauss space
We prove an isoperimetric inequality on the discrete cube which is the precise analog of a logarithmic inequality due to Talagrand. As a consequence, the Gaussian isoperimetric inequality is derived.
A Short Proof of the Gaussian Isoperimetric Inequality
We review, in a self-contained way, a short and simple proof of the Gaussian isoperimetric inequality drawn from the recent works by S. Bobkov [B2] and D. Bakry and the author [B-L].
Isoperimetric inequalities in mathematical physics
The description for this book, Isoperimetric Inequalities in Mathematical Physics. (AM-27), will be forthcoming.
Lévy–Gromov’s isoperimetric inequality for an infinite dimensional diffusion generator
Abstract. We establish, by simple semigroup arguments, a Lévy–Gromov isoperimetric inequality for the invariant measure of an infinite dimensional diffusion generator of positive curvature with
Symmetric decreasing rearrangement is sometimes continuous
This paper deals with the operation .9R 'of symmetric decreasing rearrangement which maps Wl,p (Rn) to Wi ,p (Rn) . We show that even though it is norm decreasing, .9R is not continuous for n ~ 2.
Measure theory and fine properties of functions
GENERAL MEASURE THEORY Measures and Measurable Functions Lusin's and Egoroff's Theorems Integrals and Limit Theorems Product Measures, Fubini's Theorem, Lebesgue Measure Covering Theorems
Inégalités isopérimétriques et intégrales de Dirichlet gaussiennes
© Gauthier-Villars (Éditions scientifiques et médicales Elsevier), 1984, tous droits réservés. L’accès aux archives de la revue « Annales scientifiques de l’É.N.S. » (http://www.
Steiner Symmetrization is Continuous in W1,p
Abstract. We study the continuity, smoothing, and convergence properties of Steiner symmetrization in higher space dimensions. Our main result is that Steiner symmetrization is continuous in W1,p $
Über eine von Rayleigh formulierte Minimaleigenschaft des Kreises
...
...