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Stability of parabolic Harnack inequalities
 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 spacetime 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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Cited by 30 (4 self)
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Abstract. Let (G;E) be a graph with weights faxyg for which a parabolic Harnack inequality holds with spacetime 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
, 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 nonuniform changes of the weight. We also prove necessary and sufficient conditions for the Har ..."
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Cited by 24 (2 self)
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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 nonuniform changes of the weight. We also prove necessary and sufficient conditions
HARNACK INEQUALITIES IN INFINITE DIMENSIONS
"... Abstract. We consider the Harnack inequality for harmonic functions with respect to three types of infinitedimensional 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 OrnsteinUhlenbeck ..."
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Cited by 1 (0 self)
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Abstract. We consider the Harnack inequality for harmonic functions with respect to three types of infinitedimensional 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
, 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 isoperimetrictype Harnack inequality is emphasized. Commutation properties between the heat ..."
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Cited by 4 (1 self)
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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 isoperimetrictype Harnack inequality is emphasized. Commutation properties between the heat
Harnack Inequalities and Applications for Stochastic Equations
"... We consider Harnack inequalities and their applications for the following stochastic equations (SEs). ..."
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Cited by 5 (1 self)
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We consider Harnack inequalities and their applications for the following stochastic equations (SEs).
Harnack Inequalities and Applications for OrnsteinUhlenbeck
, 2009
"... The Harnack inequality established in [11] for generalized Mehler semigroup is improved and generalized. As applications, the logHarnack inequality, the strong Feller property, the hyperbounded property, and some heat kernel inequalities are presented for a class of OU 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 logHarnack inequality, the strong Feller property, the hyperbounded property, and some heat kernel inequalities are presented for a class of OU type semigroups with jump
On the relation between elliptic and parabolic Harnack inequalities
, 2001
"... We show that, if a certain Sobolev inequality holds, then a scaleinvariant 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 ..."
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Cited by 59 (5 self)
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We show that, if a certain Sobolev inequality holds, then a scaleinvariant 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
"... 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
, 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 ..."
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Cited by 9 (0 self)
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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
, 2007
"... The aim of this article is to give an introduction to certain inequalities named after Carl ..."
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Cited by 2 (0 self)
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The aim of this article is to give an introduction to certain inequalities named after Carl
Results 1  10
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344