A PROBABILISTIC APPROACH TO DIRICHLET PROBLEMS OF SEMILINEAR ELLIPTIC PDEs WITH SINGULAR COEFFICIENTS

作者：Zhang Tusheng^*

来源：Annals of Probability, 2011, 39(4): 1502-1527.

DOI：10.1214/10-AOP591

• Dirichlet processes
• quadratic forms
• Fukushima's decomposition
• Dirichlet boundary value problems
• backward stochastic differential equations
• weak solutions
• martingale representation theorem

In this paper, we prove that there exists a unique solution to the Dirichlet boundary value problem for a general class of semilinear second order elliptic partial differential equations. Our approach is probabilistic. The theory of Dirichlet processes and backward stochastic differential equations play a crucial role.

• 出版日期2011-7