Harnack inequality and strong Feller property for stochastic fast-diffusion equations

DOI10.1016/j.jmaa.2007.12.047zbMath1151.60032arXiv0712.3136OpenAlexW2148397861MaRDI QIDQ2481876

Feng-Yu Wang, Wei Liu

Publication date: 15 April 2008

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0712.3136

zbMATH Keywords

Harnack inequalitystrong Feller propertystochastic fast-diffusion equation

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Markov semigroups and applications to diffusion processes (47D07) Applications of stochastic analysis (to PDEs, etc.) (60H30) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Transition functions, generators and resolvents (60J35)

Related Items (37)

Large deviation principle of occupation measures for non-linear monotone SPDEs ⋮ Ergodicity and Local Limits for Stochastic Local and Nonlocal $p$-Laplace Equations ⋮ Log-Harnack inequality for mild solutions of SPDEs with multiplicative noise ⋮ Harnack-type inequality for linear fractional stochastic equations ⋮ SPDE in Hilbert space with locally monotone coefficients ⋮ Irreducibility and strong Feller property for non-linear SPDEs ⋮ Harnack inequalities and heat kernel estimates for SDEs with singular drifts ⋮ Talagrand's transportation inequality for SPDEs with locally monotone drifts ⋮ Stability and moment estimates for the stochastic singular \(\Phi\)-Laplace equation ⋮ A modified log-Harnack inequality and asymptotically strong Feller property ⋮ Harnack type inequalities for SDEs driven by fractional Brownian motion with Markovian switching ⋮ Large deviation principle for a class of SPDE with locally monotone coefficients ⋮ Harnack inequality and applications for stochastic evolution equations with monotone drifts ⋮ Degenerate Fokker-Planck equations: Bismut formula, gradient estimate and Harnack inequality ⋮ Dimension-independent Harnack inequalities for subordinated semigroups ⋮ Ergodicity of transition semigroups for stochastic fast diffusion equations ⋮ Harnack inequality on configuration spaces: the coupling approach and a unified treatment ⋮ Harnack inequality for semilinear SPDE with multiplicative noise ⋮ Log-Harnack inequality for stochastic Burgers equations and applications ⋮ Existence and uniqueness of solutions to nonlinear evolution equations with locally monotone operators ⋮ Harnack inequalities and applications for Ornstein-Uhlenbeck semigroups with jump ⋮ DERIVATIVE FORMULA AND APPLICATIONS FOR HYPERDISSIPATIVE STOCHASTIC NAVIER–STOKES/BURGERS EQUATIONS ⋮ LOG-HARNACK INEQUALITY FOR STOCHASTIC DIFFERENTIAL EQUATIONS IN HILBERT SPACES AND ITS CONSEQUENCES ⋮ INVARIANCE OF SUBSPACES UNDER THE SOLUTION FLOW OF SPDE ⋮ DERIVATIVE FORMULA AND HARNACK INEQUALITY FOR DEGENERATE FUNCTIONAL SDEs ⋮ Derivative Formula and Harnack Inequality for SDEs Driven by Lévy Processes ⋮ Asymptotic log-Harnack inequality and applications for SPDE with degenerate multiplicative noise ⋮ Asymptotic couplings by reflection and applications for nonlinear monotone SPDEs ⋮ Asymptotic log-Harnack inequality and applications for stochastic 2D hydrodynamical-type systems with degenerate noise ⋮ Harnack inequality for SDE with multiplicative noise and extension to Neumann semigroup on nonconvex manifolds ⋮ On a random scaled porous media equation ⋮ Harnack inequalities for functional SDEs with multiplicative noise and applications ⋮ Large deviations for stochastic evolution equations with small multiplicative noise ⋮ Log-Harnack inequality for Gruschin type semigroups ⋮ Ergodicity of 3D Leray-α model with fractional dissipation and degenerate stochastic forcing ⋮ On the stochastic \(p\)-Laplace equation ⋮ Exponential convergence of non-linear monotone SPDEs

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Uniform positivity improving property, Sobolev inequalities, and spectral gaps
• Logarithmic Sobolev inequalities on noncompact Riemannian manifolds
• Harnack and functional inequalities for generalized Mehler semigroups.
• On the small time asymptotics of diffusion processes on path groups
• Hypercontractivity of Hamilton-Jacobi equations.
• Harnack inequality and applications for stochastic generalized porous media equations
• Stochastic generalized porous media and fast diffusion equations
• Harnack inequality and heat kernel estimates on manifolds with curvature unbounded below
• On the stochastic porous medium equation
• Heat Kernel Estimates with Application to Compactness of Manifolds
• Nash type inequalities for fractional powers of non-negative self-adjoint operators
• ON THE CAUCHY PROBLEM FOR LINEAR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS
• FUNCTIONAL INEQUALITIES, SEMIGROUP PROPERTIES AND SPECTRUM ESTIMATES
• Supercontractivity and ultracontractivity for (nonsymmetric) diffusion semigroups on manifolds
• Transition Density Estimates for Diffusion Processes on Post Critically Finite Self-Similar Fractals
• Strong Solutions of Stochastic Generalized Porous Media Equations: Existence, Uniqueness, and Ergodicity

This page was built for publication: Harnack inequality and strong Feller property for stochastic fast-diffusion equations