A regularity theory for quasi-linear Stochastic PDE<span class="math"><math><mi mathvariant="bold" is="true">s</mi></math></span> in weighted Sobolev spaces期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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A regularity theory for quasi-linear Stochastic PDE $s$ in weighted Sobolev spaces

Authors:	Ildoo Kim Kyeong-Hun Kim

Institution:	1. Center for Mathematical Challenges, Korea Institute for Advanced Study (KIAS), 85 Hoegiro Dongdaemun-gu, Seoul 130-722, Republic of Korea;2. Department of Mathematics, Korea University, 1 anam-dong sungbuk-gu, Seoul, 136-701, Republic of Korea

Abstract:	We study the second-order quasi-linear stochastic partial differential equations (SPDEs) defined on $C^{1}$ -domains. The coefficients are random functions depending on $t, x$ and the unknown solutions. We prove the uniqueness and existence of solutions in appropriate Sobolev spaces, and in addition, we obtain $L_{p}$ and Hölder estimates of both the solution and its gradient.

Keywords:	60H15 35R60 Nonlinear stochastic partial differential equations Equations of divergence type Weighted Sobolev space
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