A weighted Sobolev space theory of parabolic stochastic PDEs on non-smooth domains

DOI10.1007/s10959-012-0459-7zbMath1310.60097arXiv1109.4727OpenAlexW2066765067MaRDI QIDQ457094

Kyeong-Hun Kim

Publication date: 26 September 2014

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1109.4727

zbMATH Keywords

weighted Sobolev spacesparabolic stochastic partial differential equationsHardy inequalitynon-smooth domain

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60)

Related Items (12)

An \(L_{p}\)-estimate for the stochastic heat equation on an angular domain in \(\mathbb {R}^2\) ⋮ An \(L_p\)-maximal regularity estimate of moments of solutions to second-order stochastic partial differential equations ⋮ Neumann problem for non-divergence elliptic and parabolic equations with \(\mathrm{BMO}_x\) coefficients in weighted Sobolev spaces ⋮ Besov regularity of parabolic and hyperbolic PDEs ⋮ Singular behavior of the solution to the stochastic heat equation on a polygonal domain ⋮ Erratum to: ``An \(L_{p}\)-theory of stochastic PDEs of divergence form on Lipschitz domains ⋮ Schauder-type estimates for higher-order parabolic SPDEs ⋮ On the construction of stochastic fields with prescribed regularity by wavelet expansions ⋮ A weighted Sobolev regularity theory of the parabolic equations with measurable coefficients on conic domains in \(\mathbb{R}^d\) ⋮ Stochastic maximal regularity for rough time-dependent problems ⋮ On the regularity of the stochastic heat equation on polygonal domains in \(\mathbb{R}^2\) ⋮ Sobolev space theory and Hölder estimates for the stochastic partial differential equations on conic and polygonal domains

Cites Work

• Unnamed Item
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• An \(L_p\)-theory of SPDEs on Lipschitz domains
• On \(L_p\)-theory of stochastic partial differential equations of divergence form in \(C^1\) domains
• Linear stochastic parabolic equations, degenerating on the boundary of a domain
• On SPDEs with variable coefficients in one space dimension
• Carleson type estimates for second order elliptic equations with unbounded drift
• On stochastic partial differential equations with variable coefficients in \(C^1\) domains
• Weighted Hardy inequalities
• Hardy Inequalities
• A Sobolev Space Theory of SPDE with Constant Coefficients on a Half Line
• Weighted sobolev spaces and laplace's equation and the heat equations in a half space
• On The Sobolev Space Theory of Parabolic and Elliptic Equations inC¹Domains
• A Sobolev Space Theory of SPDEs with Constant Coefficients in a Half Space
• On $L_p $-Theory of Stochastic Partial Differential Equations in the Whole Space
• Dirichlet problem for stochasticparabolic equations in smoothdomains
• Sobolev spaces with weights in domains and boundary value problems for degenerate elliptic equations
• Some properties of traces for stochastic and deterministic parabolic weighted Sobolev spaces

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