Hypercontractivity of Hamilton–Jacobi equations
نویسندگان
چکیده
منابع مشابه
Hypercontractivity of Hamilton–jacobi Equations
– Following the equivalence between logarithmic Sobolev inequalities and hypercontractivity showed by L. Gross, we prove that logarithmic Sobolev inequalities are related similarly to hypercontractivity of solutions of Hamilton–Jacobi equations. By the infimum-convolution description of the Hamilton–Jacobi solutions, this approach provides a clear view of the connection between logarithmic Sobo...
متن کاملAsymptotic Behavior and Hypercontractivity in Nonautonomous Ornstein-uhlenbeck Equations
In this paper we investigate a class of nonautonomous linear parabolic problems with time-depending Ornstein-Uhlenbeck operators. We study the asymptotic behavior of the associated evolution operator and evolution semigroup in the periodic and non-periodic situation. Moreover, we show that the associated evolution operator is hypercontractive.
متن کاملOn Reverse Hypercontractivity
We study the notion of reverse hypercontractivity. We show that reverse hypercontractive inequalities are implied by standard hypercontractive inequalities as well as by the modified log-Sobolev inequality. Our proof is based on a new comparison lemma for Dirichlet forms and an extension of the Strook-Varapolos inequality. A consequence of our analysis is that all simple operators L = Id−E as w...
متن کاملHypercontractivity and its applications
Hypercontractive inequalities are a useful tool in dealing with extremal questions in the geometry of high-dimensional discrete and continuous spaces. In this survey we trace a few connections between different ways of stating hypercontractivity, and also present some relatively recent applications of these techniques in computer science. 1 Preliminaries and notation Fourier analysis on the hyp...
متن کاملQuantum reverse hypercontractivity
We develop reverse versions of hypercontractive inequalities for quantum channels. By generalizing classical techniques, we prove a reverse hypercontractive inequality for tensor products of qubit depolarizing channels. We apply this to obtain a rapid mixing result for depolarizing noise applied to large subspaces, and to prove bounds on a quantum generalization of non-interactive correlation d...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal de Mathématiques Pures et Appliquées
سال: 2001
ISSN: 0021-7824
DOI: 10.1016/s0021-7824(01)01208-9