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The Harnack inequality for second-order elliptic equations with divergence-free drifts
Harnack inequality second-order elliptic equations divergence-free drifts
2015/7/14
We consider an elliptic equation with a divergence-free drift b. We prove that an inequality of Harnack type holds under the assumption b ∈ Ln/2+δ ∩ L2 where δ > 0. As an application we provide a one ...
Harnack inequality for fractional sub-Laplacians in Carnot groups
Carnot groups heat kernel fractional powers of sub-Laplacian Harnack inequality
2012/6/21
In this paper we prove an invariant Harnack inequality on Carnot-Carath\'eodory balls for fractional powers of sub-Laplacians in Carnot groups. The proof relies on an "abstract" formulation of a techn...
An improved geometric inequality via vanishing moments, with applications to singular Liouville equations
Geometric PDEs Variational Methods Min-max Schemes
2012/6/14
We consider a class of singular Liouville equations on compact surfaces motivated by the study of Electroweak and Self-Dual Chern-Simons theories, the Gaussian curvature prescription with conical sing...
Stability for a GNS inequality and the Log-HLS inequality, with application to the critical mass Keller-Segel equation
GNS inequality Log-HLS inequality critical mass Keller-Segel equation Analysis of PDEs
2011/9/23
Abstract: Starting from the quantitative stability result of Bianchi and Egnell for the 2-Sobolev inequality, we deduce several different stability results for a Gagliardo-Nirenberg-Sobolev inequality...
Entropy power inequality for a family of discrete random variables
Entropy power inequality family of discrete random variables
2011/1/17
It is known that the Entropy Power Inequality (EPI) always holds if the random variables have density. Not much work has been done to identify discrete distributions for which the inequality holds wit...
Log-Harnack Inequality for Stochastic Burgers Equations and Applications
stochastic Burgers equation log-Harnack inequality strong Feller property
2010/12/14
By proving an L2-gradient estimate for the corresponding Galerkin approximations,the log-Harnack inequality is established for the semigroup associated to a class of stochastic Burgers equations. As a...
A nonlinear inequality and evolution problems
nonlinear inequality Lyapunov stability evolution problems differential equations
2010/12/15
Assume that g(t) ≥ 0, and g˙(t) ≤ −γ(t)g(t) + α(t, g(t)) + β(t), t ≥ 0; g(0) = g0; g˙ :=
dg dt,on any interval [0, T ) on which g exists and has bounded derivative from the right, g˙(t) := lims...