Results 1 - 10 of 344

Stability of parabolic Harnack inequalities

by Martin T. Barlow, Richard F. Bass - Transactions of the American Mathematical Society , 2004
"... Abstract. Let (G;E) be a graph with weights faxyg for which a parabolic Harnack inequality holds with space-time scaling exponent 2. Suppose fa0xyg is another set of weights that are comparable to faxyg. We prove that this parabolic Harnack inequality also holds for (G;E) with the weights fa0xyg. ..."
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Abstract. Let (G;E) be a graph with weights faxyg for which a parabolic Harnack inequality holds with space-time scaling exponent 2. Suppose fa0xyg is another set of weights that are comparable to faxyg. We prove that this parabolic Harnack inequality also holds for (G;E) with the weights fa0xyg

Stability results for Harnack inequalities

by Alexander Grigor'yan, Laurent Saloff-Coste , 2004
"... We develop new techniques for proving uniform elliptic and parabolic Harnack inequalities on weighted Riemannian manifolds. In particular, we prove the stability of the Harnack inequalities under certain non-uniform changes of the weight. We also prove necessary and sufficient conditions for the Har ..."
Abstract - Cited by 24 (2 self) - Add to MetaCart
We develop new techniques for proving uniform elliptic and parabolic Harnack inequalities on weighted Riemannian manifolds. In particular, we prove the stability of the Harnack inequalities under certain non-uniform changes of the weight. We also prove necessary and sufficient conditions

HARNACK INEQUALITIES IN INFINITE DIMENSIONS

by Richard F. Bass, Maria Gordina
"... Abstract. We consider the Harnack inequality for harmonic functions with respect to three types of infinite-dimensional operators. For the infinite dimensional Laplacian, we show no Harnack inequality is possible. We also show that the Harnack inequality fails for a large class of Ornstein-Uhlenbeck ..."
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Abstract. We consider the Harnack inequality for harmonic functions with respect to three types of infinite-dimensional operators. For the infinite dimensional Laplacian, we show no Harnack inequality is possible. We also show that the Harnack inequality fails for a large class of Ornstein

On Harnack inequality and optimal transportation

by D. Bakry, I. Gentil, M. Ledoux , 2013
"... Abstract. – We develop connections between Harnack inequalities for the heat flow of diffusion operators with curvature bounded from below and optimal transportation. Through heat kernel inequalities, a new isoperimetric-type Harnack inequality is emphasized. Commutation properties between the heat ..."
Abstract - Cited by 4 (1 self) - Add to MetaCart
Abstract. – We develop connections between Harnack inequalities for the heat flow of diffusion operators with curvature bounded from below and optimal transportation. Through heat kernel inequalities, a new isoperimetric-type Harnack inequality is emphasized. Commutation properties between the heat

Harnack Inequalities and Applications for Stochastic Equations

by Shun-xiang Ouyang
"... We consider Harnack inequalities and their ap-plications for the following stochastic equations (SEs). ..."
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We consider Harnack inequalities and their ap-plications for the following stochastic equations (SEs).

Harnack Inequalities and Applications for Ornstein-Uhlenbeck

by Semigroups Jump, Shun-xiang Ouyang A, Michael Röckner B, Feng-yu Wang A , 2009
"... The Harnack inequality established in [11] for generalized Mehler semigroup is improved and generalized. As applications, the log-Harnack inequality, the strong Feller property, the hyper-bounded property, and some heat kernel inequalities are presented for a class of O-U type semigroups with jump. ..."
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The Harnack inequality established in [11] for generalized Mehler semigroup is improved and generalized. As applications, the log-Harnack inequality, the strong Feller property, the hyper-bounded property, and some heat kernel inequalities are presented for a class of O-U type semigroups with jump

On the relation between elliptic and parabolic Harnack inequalities

by W. Hebisch, L. Saloff-Coste , 2001
"... We show that, if a certain Sobolev inequality holds, then a scale-invariant elliptic Harnack inequality suces to imply its a priori stronger parabolic counterpart. Neither the relative Sobolev inequality nor the elliptic Harnack inequality alone suces to imply the parabolic Harnack inequality in que ..."
Abstract - Cited by 59 (5 self) - Add to MetaCart
We show that, if a certain Sobolev inequality holds, then a scale-invariant elliptic Harnack inequality suces to imply its a priori stronger parabolic counterpart. Neither the relative Sobolev inequality nor the elliptic Harnack inequality alone suces to imply the parabolic Harnack inequality

HARNACK INEQUALITY FOR NONLINEAR WEIGHTED EQUATIONS

by Nedra Belhaj Rhouma, Mahel Mosbah
"... In this paper, we prove the Harnack inequality for nonnegative weak solutions of the following nonlinear subelliptic equation −divA(x,u,∇u) = f(x,u,∇u). 1 ..."
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In this paper, we prove the Harnack inequality for nonnegative weak solutions of the following nonlinear subelliptic equation −divA(x,u,∇u) = f(x,u,∇u). 1

Some remarks on the elliptic Harnack inequality

by Martin T. Barlow , 2003
"... In this note we give three short results concerning the elliptic Harnack inequality (EHI), in the context of random walks on graphs. The first is that the EHI implies polynomial growth of the number of points in balls, and the second that the EHI is equivalent to an annulus type Harnack inequality f ..."
Abstract - Cited by 9 (0 self) - Add to MetaCart
In this note we give three short results concerning the elliptic Harnack inequality (EHI), in the context of random walks on graphs. The first is that the EHI implies polynomial growth of the number of points in balls, and the second that the EHI is equivalent to an annulus type Harnack inequality

Harnack Inequalities: an introduction

by Moritz Kassmann , 2007
"... The aim of this article is to give an introduction to certain inequalities named after Carl ..."
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The aim of this article is to give an introduction to certain inequalities named after Carl
Results 1 - 10 of 344