On Cauchy—Dirichlet Problem for Parabolic Quasilinear SPDEs

被引：0

作者：

R. Mikulevicius

H. Pragarauskas

机构：

[1] Intitute of Mathematics and Informatics,

来源：

Potential Analysis | 2006年 / 25卷

关键词：

Primary 60H15; Secondary 35K15; Parabolic stochastic partial differential equations; Cauchy–Dirichlet problem; Schauder apriori estimates; weighted Hölder spaces;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We study the Cauchy–Dirichlet problem for a second-order quasilinear parabolic stochastic differential equation (SPDE) in a domain with a zero order noise term driven by a cylindrical Brownian motion. Considering its solution as a function with values in a probability space and using the methods of deterministic partial differential equations, we establish the existence and uniqueness of a strong solution in Hölder classes with weights.

引用

页码：37 / 75

页数：38

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