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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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

Permanent link to this document
http://projecteuclid.org/euclid.ejp/1465062362

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

Mathematical Reviews number (MathSciNet)
MR2928723

Zentralblatt MATH identifier
1261.60068

Subjects
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

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

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

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


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References

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