Schauder estimates for elliptic equations in Banach spaces associated with stochastic reaction-diffusion equations

被引：8

作者：

Cerrai, Sandra ^{[1
]}

Da Prato, Giuseppe ^{[2
]}

机构：

[1] Univ Maryland, College Pk, MD 20742 USA

[2] Scuola Normale Super Pisa, I-56126 Pisa, Italy

来源：

JOURNAL OF EVOLUTION EQUATIONS | 2012年 / 12卷 / 01期

基金：

美国国家科学基金会;

关键词：

Stochastic reaction-diffusion equations; Schauder estimates; Brownian Sheet; interpolation; SEMIGROUPS;

D O I：

10.1007/s00028-011-0124-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider some reaction-diffusion equations perturbed by white noise and prove Schauder estimates for the elliptic problem associated with the generator of the corresponding transition semigroup, defined in the Banach space of continuous functions. This requires the proof of some new interpolation result.

引用

页码：83 / 98

页数：16

共 18 条

[1]

Alvino A., 1996, RES NOTES MATH, V350, P100

[2]

[Anonymous], 2002, LONDON MATH SOC LECT

[3] Infinite dimensional stochastic differential equations of Ornstein-Uhlenbeck type [J].