Dirichlet boundary value problems for elliptic operators with measure data: a probabilistic approach

2018/04/05 by Saisai Yang, Tusheng Zhang, Yang, Saisai +1
Computer Science · Mathematics · #37L55 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Primary 60H15 Secondary 35R60 #Probability (math.PR) #math.PR #msc:35R60 #msc:37L55 #msc:60H15

paper · pdf · doi:10.48550/arxiv.1804.01819

arxiv created 2018/04/05 · openalex publication_date 2018/04/05 · arxiv updated 2018/04/06 · openalex created_date 2018/04/13 · openalex updated_date 2026/07/28

Abstract

In this paper, we use probabilistic approach to prove that there exists a unique weak solution to the Dirichlet boundary value problem for second order elliptic equations whose coefficients are signed measures, and we will give a probabilistic representation of the solutions. This is the first time to study Dirichlet boundary value problems with this generality. The heat kernel estimates play a crucial role in our approach.

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