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Probabilistic interpretation of a system of quasilinear elliptic partial differential equations under Neumann boundary conditions

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  • Hu, Ying

Abstract

A probabilistic interpretation of a system of second order quasilinear elliptic partial differential equations under a Neumann boundary condition is obtained by introducing a kind of backward stochastic differential equations in the infinite horizon case. In the same time, a simple proof for the existence and uniqueness result of the classical solution of that Neumann problem is given.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:48:y:1993:i:1:p:107-121
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    Cited by:

    1. 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.
    2. Maticiuc, Lucian & Rascanu, Aurel, 2010. "A stochastic approach to a multivalued Dirichlet-Neumann problem," Stochastic Processes and their Applications, Elsevier, vol. 120(6), pages 777-800, June.
    3. Maticiuc, Lucian & Răşcanu, Aurel, 2016. "On the continuity of the probabilistic representation of a semilinear Neumann–Dirichlet problem," Stochastic Processes and their Applications, Elsevier, vol. 126(2), pages 572-607.
    4. Anis Matoussi & Michael Scheutzow, 2002. "Stochastic PDEs Driven by Nonlinear Noise and Backward Doubly SDEs," Journal of Theoretical Probability, Springer, vol. 15(1), pages 1-39, January.

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