## Electronic Journal of Probability

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

#### Abstract

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

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

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

https://projecteuclid.org/euclid.ejp/1465062362

Digital Object Identifier
doi:10.1214/EJP.v17-2062

Mathematical Reviews number (MathSciNet)
MR2928723

Zentralblatt MATH identifier
1261.60068

Rights

#### Citation

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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