Local \(L_\infty\)-estimates, weak Harnack inequality, and stochastic continuity of solutions of SPDEs

DOI10.1016/j.jde.2016.09.038zbMath1356.60099arXiv1503.04472OpenAlexW2528660392MaRDI QIDQ338463

Máté Gerencsér, Konstantinos Anastasios Dareiotis

Publication date: 4 November 2016

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1503.04472

zbMATH Keywords

stochastic PDEsweak Harnack inequalityDe Giorgi iterationlocal \(L_\infty\)-estimatesstochastic continuity

Mathematics Subject Classification ID

Stochastic partial differential equations (aspects of stochastic analysis) (60H15)

Related Items

A probabilistic Harnack inequality and strict positivity of stochastic partial differential equations ⋮ \(L^2\)-theory of linear degenerate SPDEs and \(L^p ( p > 0)\) estimates for the uniform norm of weak solutions ⋮ Existence of strong solutions for Itô's stochastic equations via approximations: revisited ⋮ Supremum estimates for degenerate, quasilinear stochastic partial differential equations

Cites Work

• On the Itô--Wentzell formula for distribution-valued processes and related topics
• Non-divergence parabolic equations of second order with critical drift in Lebesgue spaces
• Maximum principle for quasi-linear backward stochastic partial differential equations
• Stochastic De Giorgi iteration and regularity of stochastic partial differential equations
• \(L_p\)-estimates for SPDE with discontinuous coefficients in domains
• \(L^2\)-theory of linear degenerate SPDEs and \(L^p ( p > 0)\) estimates for the uniform norm of weak solutions
• On the boundedness of solutions of SPDEs
• Continuity of Solutions of Parabolic and Elliptic Equations
• Regularity theory for fully nonlinear integro-differential equations
• On Harnack's theorem for elliptic differential equations
• ON STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS
• Harnack Inequalities for Stochastic Partial Differential Equations
• A Regularity Result for Quasilinear Stochastic Partial Differential Equations of Parabolic Type
• A harnack inequality for parabolic differential equations
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item