On \(L_p\)-theory of stochastic partial differential equations of divergence form in \(C^1\) domains

DOI10.1007/s00440-004-0368-5zbMath1066.60063OpenAlexW1997384891MaRDI QIDQ1765115

Kyeong-Hun Kim

Publication date: 22 February 2005

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00440-004-0368-5

zbMATH Keywords

Sobolev spaces with weights

Mathematics Subject Classification ID

Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60)

Related Items (19)

Elliptic and parabolic equations with measurable coefficients in weighted Sobolev spaces ⋮ \(L^{p}\)-theory of semi-linear SPDEs on general measure spaces and applications ⋮ Nonlinear parabolic stochastic evolution equations in critical spaces Part I. Stochastic maximal regularity and local existence* ⋮ A regularity theory for quasi-linear stochastic PDE\(\mathbf{s}\) in weighted Sobolev spaces ⋮ A Sobolev space theory for parabolic stochastic PDEs driven by Lévy processes on \(C^1\)-domains ⋮ A weighted Sobolev space theory of parabolic stochastic PDEs on non-smooth domains ⋮ An Itô formula for rough partial differential equations and some applications ⋮ A weighted \(L_p\)-theory for divergence type parabolic PDEs with BMO coefficients on \(C^1\)-domains ⋮ Schauder-type estimates for higher-order parabolic SPDEs ⋮ A weighted Sobolev space theory for the diffusion-wave equations with time-fractional derivatives on \(C^1\) domains ⋮ Regularities for semilinear stochastic partial differential equations ⋮ Some \(L_p\) and Hölder estimates for divergence type nonlinear SPDEs on \(C^1\)-domains ⋮ Sobolev space theory of SPDEs with continuous or measurable leading coefficients ⋮ \(W^{2, p}\)-solutions of parabolic SPDEs in general domains ⋮ An \(L_{p}\)-theory of stochastic PDEs of divergence form on Lipschitz domains ⋮ Stochastic maximal regularity for rough time-dependent problems ⋮ On divergence form SPDEs with VMO coefficients in a half space ⋮ Sobolev space theory and Hölder estimates for the stochastic partial differential equations on conic and polygonal domains ⋮ \(L^p\)-strong solutions of stochastic partial differential equations with monotonic drifts

Cites Work

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• Intermediate Schauder estimates
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• On stochastic partial differential equations with variable coefficients in \(C^1\) domains
• Weighted sobolev spaces and laplace's equation and the heat equations in a half space
• Holder Estimates for Solutions of Parabolic SPDEs
• On The Sobolev Space Theory of Parabolic and Elliptic Equations inC¹Domains
• A Sobolev Space Theory of SPDEs with Constant Coefficients in a Half Space
• OnL_p-Theory of stochastic partialdifferential equations of divergence form with continuous coefficients
• 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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