Log-Harnack inequality for stochastic Burgers equations and applications

F.Y. Wang, J.L. Wu, L. Xu

Research output: Contribution to journalArticleAcademicpeer-review

17 Citations (Scopus)

Abstract

By proving an L^2-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 applications, we derive the strong Feller property of the semigroup, the irreducibility of the solution, the entropy-cost inequality for the adjoint semigroup, and entropy upper bounds of the transition density.
Original languageEnglish
Pages (from-to)151-159
JournalJournal of Mathematical Analysis and Applications
Volume384
Issue number1
DOIs
Publication statusPublished - 2011

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Harnack Inequality
Burgers Equation
Stochastic Equations
Entropy
Semigroup
Strong Feller Property
Gradient Estimate
Transition Density
Galerkin Approximation
Irreducibility
Upper bound
Costs

Cite this

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title = "Log-Harnack inequality for stochastic Burgers equations and applications",
abstract = "By proving an L^2-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 applications, we derive the strong Feller property of the semigroup, the irreducibility of the solution, the entropy-cost inequality for the adjoint semigroup, and entropy upper bounds of the transition density.",
author = "F.Y. Wang and J.L. Wu and L. Xu",
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Log-Harnack inequality for stochastic Burgers equations and applications. / Wang, F.Y.; Wu, J.L.; Xu, L.

In: Journal of Mathematical Analysis and Applications, Vol. 384, No. 1, 2011, p. 151-159.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Log-Harnack inequality for stochastic Burgers equations and applications

AU - Wang, F.Y.

AU - Wu, J.L.

AU - Xu, L.

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N2 - By proving an L^2-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 applications, we derive the strong Feller property of the semigroup, the irreducibility of the solution, the entropy-cost inequality for the adjoint semigroup, and entropy upper bounds of the transition density.

AB - By proving an L^2-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 applications, we derive the strong Feller property of the semigroup, the irreducibility of the solution, the entropy-cost inequality for the adjoint semigroup, and entropy upper bounds of the transition density.

U2 - 10.1016/j.jmaa.2011.02.032

DO - 10.1016/j.jmaa.2011.02.032

M3 - Article

VL - 384

SP - 151

EP - 159

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

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