SPDEs with non-Lipschitz coefficients and nonhomogeneous boundary conditions

被引：1

作者：

Xiong, Jie ^{[1
,2
]}

Yang, Xu ^{[3
]}

机构：

[1] Southern Univ Sci & Technol, Dept Math, Shenzhen, Peoples R China

[2] Southern Univ Sci & Technol, SUSTech Int Ctr Math, Shenzhen, Peoples R China

[3] North Minzu Univ, Sch Math & Informat Sci, Yinchuan, Ningxia, Peoples R China

来源：

BERNOULLI | 2023年 / 29卷 / 04期

关键词：

Boundary conditions; comparison theorem; Holder continuity; non-Lipschitz coefficients; pathwise uniqueness; stochastic partial differential equation; PARTIAL-DIFFERENTIAL EQUATIONS; WHITE-NOISE; PATHWISE UNIQUENESS; STOCHASTIC-EQUATIONS; INVARIANT-MEASURES; HOLDER CONTINUITY; JOINT CONTINUITY; PARABOLIC SPDES; NONLINEAR SPDES; DRIVEN;

D O I：

10.3150/22-BEJ1571

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this article, we consider a stochastic partial differential equation (SPDE) driven by Gaussian colored noise with Dirichlet, Neumann or mixed nonhomogeneous random boundary conditions when the drift and diffusion coefficients are non-Lipschitz. We prove the existence of a unique strong solution to this SPDE and obtain a comparison theorem between such SPDEs. We also study the Holder continuity of the solution in both time and space variables, and find the dependence of the Holder exponent on that of the Dirichlet boundary.

引用

页码：2987 / 3012

页数：26

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