Electronic Journal of Probability

Stochastic representation of entropy solutions of semilinear elliptic obstacle problems with measure data

Andrzej Rozkosz and Leszek Slominski

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We consider semilinear obstacle problem with measure data associated with uniformly elliptic divergence form operator. We prove existence and uniqueness of entropy solution of the problem and provide stochastic representation of the solution in terms of some generalized reflected backward stochastic differential equations with random terminal time.

Article information

Electron. J. Probab., Volume 17 (2012), paper no. 40, 27 pp.

Accepted: 31 May 2012
First available in Project Euclid: 4 June 2016

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Zentralblatt MATH identifier

Primary: 60H99: None of the above, but in this section
Secondary: 35J87: Nonlinear elliptic unilateral problems and nonlinear elliptic variational inequalities [See also 35R35, 49J40] 35R06: Partial differential equations with measure

backward stochastic differential equation semilinear elliptic obstacle problem measure data entropy solution

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Rozkosz, Andrzej; Slominski, Leszek. Stochastic representation of entropy solutions of semilinear elliptic obstacle problems with measure data. Electron. J. Probab. 17 (2012), paper no. 40, 27 pp. doi:10.1214/EJP.v17-2062. https://projecteuclid.org/euclid.ejp/1465062362

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