A probabilistic approach to Neumann problems for elliptic PDEs with nonlinear divergence terms

Chi Hong Wong, Xue Yang and Jing Zhang

Stochastic Processes and their Applications, 2022, vol. 151, issue C, 101-126

Abstract: By a probabilistic method, we prove the existence and uniqueness of weak solutions to Neumann problems for a class of semi-linear elliptic partial differential equations with nonlinear singular divergence terms, which can only be understood in distributional sense. This leads to the further study on a new class of infinite horizon backward stochastic differential equations, which involves integrals with respect to a forward–backward martingale and a singular continuous increasing process.

Keywords: Elliptic partial differential equation; Neumann boundary condition; Backward stochastic differential equation; Dirichlet form; Martingale decomposition (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:151:y:2022:i:c:p:101-126

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DOI: 10.1016/j.spa.2022.06.004

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