扩散方程的具有振动边值的Dirichlet问题

The Vibration Border Function Dirichlet Problem for the Diffusion Equation

令.D表示d+1维欧氏空间R.d的有界子集.利用概率方法和时空布朗运动,对.D上如下扩散方程21Δu(.x(t))+q(.x(t))u(.x(t))=tu(.x(t)),.x(t)∈.D的随机Dirichlet问题进行了推广,其中q是给定的定义在D.上的有界H lder连续函数.证明了上述扩散方程具有振动边值的Dirichlet问题的存在性.

Let D be a bounded domain in the d ＋ 1-dimensional Euclidean space Rd. A probabilistic treatment of the generalization of the Dirichlet problem is given for the following diffusion equation 1/2△u（x（t））＋q（x（t））u（x（t））=δ/δu（x（t））,x（t）∈（D）where q is a bounded H61der continuous function. The existence of the solution of the vibration border function Dirichlet problem for the diffusion equation is proved.