Mixed Boundary Value Problems of Semilinear Elliptic PDEs and BSDEs with Singular Coefficients

2011/12/14 by Xue Yang, Tusheng Zhang, Yang, Xue +1
Economics, Econometrics and Finance · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Probability (math.PR) #Stochastic processes and financial applications #advanced mathematical theories #math.AP #math.PR

paper · pdf · doi:10.48550/arxiv.1112.3148

arxiv created 2011/12/14 · openalex publication_date 2011/12/14 · arxiv updated 2011/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove that there exists a unique weak solution to the mixed boundary value problem for a general class of semilinear second order elliptic partial differential equations with singular coefficients. Our approach is probabilistic. The theory of Dirichlet forms and backward stochastic differential equations with singular coefficients and infinite horizon plays a crucial role.

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