An \(L_{p}\)-estimate for the stochastic heat equation on an angular domain in \(\mathbb {R}^2\)

DOI10.1007/s40072-017-0102-9zbMath1402.60075arXiv1603.08908OpenAlexW3124329399WikidataQ115375225 ScholiaQ115375225MaRDI QIDQ1617252

Petru A. Cioica-Licht, Felix Lindner, Kyeong-Hun Kim, Kijung Lee

Publication date: 7 November 2018

Published in: Stochastic and Partial Differential Equations. Analysis and Computations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1603.08908

zbMATH Keywords

corner singularitystochastic heat equationstochastic partial differential equationnon-smooth domainangular domainweighted \(L_{p}\)-estimateweighted Sobolev regularity

Mathematics Subject Classification ID

Heat equation (35K05) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60)

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Nonlinear parabolic stochastic evolution equations in critical spaces Part I. Stochastic maximal regularity and local existence* ⋮ On the 𝐿_{𝑝}-boundedness of the stochastic singular integral operators and its application to 𝐿_{𝑝}-regularity theory of stochastic partial differential equations ⋮ Stochastic maximal regularity for rough time-dependent problems ⋮ A refined Green's function estimate of the time measurable parabolic operators with conic domains ⋮ 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 ⋮ Elliptic and parabolic boundary value problems in weighted function spaces

Cites Work

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• Asymptotics of solutions of the heat equation in cones and dihedra under minimal assumptions on the boundary
• On the \(L_q(L_p)\)-regularity and Besov smoothness of stochastic parabolic equations on bounded Lipschitz domains
• Stochastic maximal \(L^{p}\)-regularity
• A weighted Sobolev space theory of parabolic stochastic PDEs on non-smooth domains
• Singular behavior of the solution to the stochastic heat equation on a polygonal domain
• Maximal \(L^{p}\)-regularity for the Laplacian on Lipschitz domains
• Elliptic boundary value problems on corner domains. Smoothness and asymptotics of solutions
• On asymptotics of the Green function and Poisson kernels of a mixed parabolic problem in a cone. II
• Maximal regularity for stochastic convolutions in \(L^p\) spaces
• A \(W_ 2^ n\)-theory of the Dirichlet problem for SPDEs in general smooth domains
• Singular behavior of elliptic problems in non Hilbertian Sobolev spaces
• On stochastic partial differential equations with variable coefficients in \(C^1\) domains
• Maximal $L^p$-Regularity for Stochastic Evolution Equations
• Dirichlet boundary value problem for stochastic parabolic equations: compatibility relations and regularity of solutions
• A Sobolev Space Theory of SPDE with Constant Coefficients on a Half Line
• On stochastic convolution in banach spaces and applications
• On The Sobolev Space Theory of Parabolic and Elliptic Equations inC¹Domains
• A Sobolev Space Theory of SPDEs with Constant Coefficients in a Half Space
• Stochastic Equations in Infinite Dimensions
• 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