Electronic Journal of Probability

Sobolev solution for semilinear PDE with obstacle under monotonicity condition

Anis Matoussi and Mingyu Xu

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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

Article information

Electron. J. Probab., Volume 13 (2008), paper no. 35, 1035-1067.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35D05
Secondary: 60H10: Stochastic ordinary differential equations [See also 34F05] 60H30B

Backward stochastic differential equation Reflected backward stochastic differential equation monotonicity condition Stochastic flow partial differential equation with obstacle

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Matoussi, Anis; Xu, Mingyu. Sobolev solution for semilinear PDE with obstacle under monotonicity condition. Electron. J. Probab. 13 (2008), paper no. 35, 1035--1067. doi:10.1214/EJP.v13-522. https://projecteuclid.org/euclid.ejp/1464819108

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