一类Ornstein-Uhlenbeck算子的狄利克雷问题

Dirichlet Problem for a Kind of Ornstein-Uhlenbeck Operator

该文研究一类Ornstein-Uhlenbeck算子的狄利克雷问题,通过运用Galerkin近似法、Minty法得到该类Ornstein-Uhlenbeck算子的狄利克雷问题弱解的存在唯一性,进而证明了其弱解的连续性.

This paper studies the Dirichlet problem of a class of Ornstein-Uhlenbeck operators,obtains the existence and uniqueness of the weak solution of the Dirichlet problem of this class of Ornstein-Uhlenbeck operators by using Galerkin approximation method and Minty method,and then proves the continuity of the weak solutions.