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

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  • Wong, Chi Hong
  • Yang, Xue
  • Zhang, Jing

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.

Suggested Citation

  • Wong, Chi Hong & Yang, Xue & Zhang, Jing, 2022. "A probabilistic approach to Neumann problems for elliptic PDEs with nonlinear divergence terms," Stochastic Processes and their Applications, Elsevier, vol. 151(C), pages 101-126.
    • Handle: RePEc:eee:spapps:v:151:y:2022:i:c:p:101-126
    DOI: 10.1016/j.spa.2022.06.004
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    References listed on IDEAS

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    1. Hu, Ying, 1993. "Probabilistic interpretation of a system of quasilinear elliptic partial differential equations under Neumann boundary conditions," Stochastic Processes and their Applications, Elsevier, vol. 48(1), pages 107-121, October.
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