%0 Journal Article
%T Existence of Weak Solutions to a Class of Elliptic Stochastic Partial Differential Equations<br>一类椭圆型随机偏微分方程弱解的存在性
%A Ran Qikang
%A <br>冉启康
%J 数学物理学报(A辑)
%D 2008
%I 
%X In this paper the authors study of following problem: Let $D$ be a bounded open set of $R^N(N>1)$ and $(\Omega,F,P)$ is a probability space. The authors study the existence of weak solutions of the following stochastic boundary value problem:$$\left\{\begin{array}{ll}-{\rm div} A(x,\omega,u, \nabla u)=f(x,\omega, u),\,\, &(x,\omega)\in D\times \Omega,\\u=0, &(x,\omega)\in \partial D\times \Omega,\end{array}\right.$$where by div and $\nabla$ the authors denote differentiation with respect to $x$ only. First, the authorsintroduce the concept of the weak solution, then the authors transform the stochastic problem into a deterministicone in high-dimensions. Finally, the authors prove the existence of weak solutions.
%K Nonlinear elliptic stochastic partial differential equationszz
%K Weak solutionszz
%K Leray-Schauder continuation methodzz<br>非线性椭圆随机偏微分方程
%K 弱解
%K Leray-Schauder连续方法.
%K 椭圆型
%K 随机偏微分方程
%K 弱解的存在性
%K Partial
%K Differential
%K Equations
%K Stochastic
%K Elliptic
%K Class
%K Weak
%K Solutions
%K 确定性问题
%K 随机问题
%K 转化
%K divA
%K 边值问题
%K 研究
%K 概率空间
%K 开集
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=37F46C35E03B4B86&jid=4DB553CDB5F521D8C921082E5C95EC80&aid=EADA9586CDA1315549673A77DB3B0489&yid=67289AFF6305E306&vid=D3E34374A0D77D7F&iid=0B39A22176CE99FB&sid=CA9ED1AB4D9E3E04&eid=A5B34D9E8FDA439A&journal_id=1003-3998&journal_name=数学物理学报(A辑)&referenced_num=0&reference_num=12