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arXiv · 1805.06586

$W^{2,p}$-solutions of parabolic SPDEs in general domains

Kai Du
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Abstract

The Dirichlet problem for a class of stochastic partial differential equations is studied in Sobolev spaces. The existence and uniqueness result is proved under certain compatibility conditions that ensure the finiteness of $L^{p}(\Omega\times(0,T),W^{2,p}(G))$-norms of solutions. The H\"older continuity of solutions and their derivatives is also obtained by embedding.

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Kai Du. 2018-05-17. $W^{2,p}$-solutions of parabolic SPDEs in general domains. https://arxiv.org/abs/1805.06586

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