A regularity theory for quasi-linear stochastic PDE\(\mathbf{s}\) in weighted Sobolev spaces

DOI10.1016/j.spa.2017.06.006zbMath1380.60059arXiv1705.01717OpenAlexW2733484890MaRDI QIDQ1688620

Kyeong-Hun Kim, Ildoo Kim

Publication date: 11 January 2018

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1705.01717

zbMATH Keywords

weighted Sobolev spacenonlinear stochastic partial differential equationsequations of divergence type

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 (5)

\(L_p\)-regularity theory for semilinear stochastic partial differential equations with multiplicative white noise ⋮ Nonlinear parabolic stochastic evolution equations in critical spaces Part I. Stochastic maximal regularity and local existence* ⋮ \(L^p\)-estimates and regularity for SPDEs with monotone semilinearity ⋮ Boundary behavior and interior Hölder regularity of the solution to nonlinear stochastic partial differential equation driven by space-time white noise ⋮ Stochastic maximal regularity for rough time-dependent problems

Cites Work

• Stochastic partial differential equations: an introduction
• Sobolev space theory of SPDEs with continuous or measurable leading coefficients
• Intermediate Schauder estimates
• On the unique solvability of some nonlinear stochastic PDEs
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• Linear stochastic parabolic equations, degenerating on the boundary of a domain
• \(L_{q}\) (\(L_{p}\)) theory and Hölder estimates for parabolic SPDEs
• Some \(L_p\) and Hölder estimates for divergence type nonlinear SPDEs on \(C^1\)-domains
• 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
• Fully Nonlinear Stochastic Partial Differential Equations
• Stochastic evolution equations
• 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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