Probabilistic representations of solutions of elliptic boundary value problem and non-symmetric semigroups

2014/07/16 by Chuanzhong Chen, Chuan-Zhong Chen, Chen, Chuan-Zhong +4
Computer Science · Mathematics · #35J25 #35R05 #60H30 #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #math.AP #msc:35J25 #msc:35R05 #msc:60H30

paper · pdf · doi:10.48550/arxiv.1407.4185

openalex publication_date 2014/07/16 · arxiv created 2015/04/16 · arxiv updated 2015/04/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper, we use a probabilistic approach to show that there exists a unique, bounded continuous solution to the Dirichlet boundary value problem for a general class of second order non-symmetric elliptic operators L with singular coefficients, which does not necessarily have the maximum principle. The theory of Dirichlet forms and heat kernel estimates play a crucial role in our approach. A probabilistic representation of the non-symmetric semigroup \T_t\_{t≥ 0} generated by L is also given.

Citations

• A New Approach to Absolute Continuity of Elliptic Measure, with Applications to Non-symmetric Equations

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