On the equivalence of heat kernel estimates and logarithmic Sobolev inequalities for the Hodge Laplacian
نویسندگان
چکیده
منابع مشابه
Heat kernel estimates for the fractional Laplacian
Explicit sharp estimates for the Green function of the Laplacian in C domains were completed in 1986 by Zhao [42]. Sharp estimates of the Green function of Lipschitz domains were given in 2000 by Bogdan [6]. Explicit qualitatively sharp estimates for the classical heat kernel in C domains were established in 2002 by Zhang [41]. Qualitatively sharp heat kernel estimates in Lipschitz domains were...
متن کاملOn the equivalence of parabolic Harnack inequalities and heat kernel estimates
We prove the equivalence of parabolic Harnack inequalities and sub-Gaussian heat kernel estimates in a general metric measure space with a local regular Dirichlet form.
متن کاملHeat Kernel Estimates for Dirichlet Fractional Laplacian
In this paper, we consider the fractional Laplacian −(−∆)α/2 on an open subset in R with zero exterior condition. We establish sharp two-sided estimates for the heat kernel of such Dirichlet fractional Laplacian in C open sets. This heat kernel is also the transition density of a rotationally symmetric α-stable process killed upon leaving a C open set. Our results are the first sharp two-sided ...
متن کاملHeat kernel estimates for the Dirichlet fractional Laplacian
Abstract. We consider the fractional Laplacian −(−1)α/2 on an open subset in Rd with zero exterior condition. We establish sharp two-sided estimates for the heat kernel of such a Dirichlet fractional Laplacian inC1,1 open sets. This heat kernel is also the transition density of a rotationally symmetric α-stable process killed upon leaving a C1,1 open set. Our results are the first sharp twoside...
متن کاملLogarithmic Sobolev Inequalities and the Information Theory
In this paper we present an overview on logarithmic Sobolev inequalities. These inequalities have become a subject of intense research activity during the past years, from analysis and geometry in finite and infinite dimension, to probability and statistical mechanics, and of course many others developments and applications are expected. We have divided this paper into three parts. The first pa...
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 of Differential Equations
سال: 2007
ISSN: 0022-0396
DOI: 10.1016/j.jde.2006.10.007