Regularities for semilinear stochastic partial differential equations

Xicheng Zhang

doi:10.1016/j.jfa.2007.03.018

Regularities for semilinear stochastic partial differential equations

Xicheng Zhang^*

^*Corresponding author for this work

Bielefeld University
Huazhong University of Science and Technology

Research output: Contribution to journal › Article › peer-review

18 Citations (Scopus)

Abstract

In this paper, we study the regularities of solutions to semilinear stochastic partial differential equations in general settings, and prove that the solution can be smooth arbitrarily when the data is sufficiently regular. As applications, we also study several classes of semilinear stochastic partial differential equations on abstract Wiener space, complete Riemannian manifold as well as bounded domain in Euclidean space.

Original language	English
Pages (from-to)	454-476
Number of pages	23
Journal	Journal of Functional Analysis
Volume	249
Issue number	2
DOIs	https://doi.org/10.1016/j.jfa.2007.03.018
Publication status	Published - 15 Aug 2007
Externally published	Yes

Keywords

Nonlinear interpolation
Regularity
Stochastic partial differential equation

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10.1016/j.jfa.2007.03.018

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title = "Regularities for semilinear stochastic partial differential equations",

abstract = "In this paper, we study the regularities of solutions to semilinear stochastic partial differential equations in general settings, and prove that the solution can be smooth arbitrarily when the data is sufficiently regular. As applications, we also study several classes of semilinear stochastic partial differential equations on abstract Wiener space, complete Riemannian manifold as well as bounded domain in Euclidean space.",

keywords = "Nonlinear interpolation, Regularity, Stochastic partial differential equation",

author = "Xicheng Zhang",

year = "2007",

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doi = "10.1016/j.jfa.2007.03.018",

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T1 - Regularities for semilinear stochastic partial differential equations

AU - Zhang, Xicheng

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N2 - In this paper, we study the regularities of solutions to semilinear stochastic partial differential equations in general settings, and prove that the solution can be smooth arbitrarily when the data is sufficiently regular. As applications, we also study several classes of semilinear stochastic partial differential equations on abstract Wiener space, complete Riemannian manifold as well as bounded domain in Euclidean space.

AB - In this paper, we study the regularities of solutions to semilinear stochastic partial differential equations in general settings, and prove that the solution can be smooth arbitrarily when the data is sufficiently regular. As applications, we also study several classes of semilinear stochastic partial differential equations on abstract Wiener space, complete Riemannian manifold as well as bounded domain in Euclidean space.

KW - Nonlinear interpolation

KW - Regularity

KW - Stochastic partial differential equation

UR - https://www.scopus.com/pages/publications/34250644049

U2 - 10.1016/j.jfa.2007.03.018

DO - 10.1016/j.jfa.2007.03.018

M3 - Article

AN - SCOPUS:34250644049

SN - 0022-1236

VL - 249

SP - 454

EP - 476

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 2

ER -

Regularities for semilinear stochastic partial differential equations

Abstract

Keywords

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