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2008 Sobolev solution for semilinear PDE with obstacle under monotonicity condition
Anis Matoussi, Mingyu Xu
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Electron. J. Probab. 13: 1035-1067 (2008). DOI: 10.1214/EJP.v13-522


We prove the existence and uniqueness of Sobolev solution of a semilinear PDE's and PDE's with obstacle under monotonicity condition. Moreover we give the probabilistic interpretation of the solutions in term of Backward SDE and reflected Backward SDE respectively


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Anis Matoussi. Mingyu Xu. "Sobolev solution for semilinear PDE with obstacle under monotonicity condition." Electron. J. Probab. 13 1035 - 1067, 2008.


Accepted: 29 June 2008; Published: 2008
First available in Project Euclid: 1 June 2016

zbMATH: 1191.35133
MathSciNet: MR2424986
Digital Object Identifier: 10.1214/EJP.v13-522

Primary: 35D05
Secondary: 60H10 , 60H30B

Keywords: backward stochastic differential equation , monotonicity condition , partial differential equation with obstacle , reflected backward stochastic differential equation , stochastic flow

Vol.13 • 2008
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