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

Electronic Journal of Probability

Volumn 17, Issue , 2012, Pages 1-27

  Rozkoszy, Andrzej ^a   Słomińskiy, Leszek ^a  

^a NICOLAUS COPERNICUS UNIVERSITY   (Poland)

Author keywords

Backward stochastic differential equation; Entropy solution; Measure data; Semilinear elliptic obstacle problem

Indexed keywords

EID: 84863429955     PISSN: None     EISSN: 10836489     Source Type: Journal    
DOI: 10.1214/EJP.v17-2062     Document Type: Article

References (20)

1. 1-theory of existence and uniqueness of solutions of nonlinear elliptic equations. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 22, (1995), 241-273. MR-1354907
2. Boccardo, L., Gallouët, T.: Non-linear Elliptic and Parabolic Equations Involving Measure Data. J. Funct. Anal. 87, (1989), 149-169. MR-1025884
3. Boccardo, L., Gallouët, T., Orsina, L.: Existence and uniqueness of entropy solutions for nonlinear elliptic equations with measure data. Ann. Inst. H. Poincaré Anal. Non Linéaire 13, (1996), 539-551. MR-1409661
4. p solutions of backward stochastic differential equations. Stochastic Process. Appl. 108, (2003), 109-129. MR-2008603
5. Chung, K.L., Zhao, Z.: From Brownian Motion to Schrödinger's Equation. Springer-Verlag, Berlin, 1995. xii+287 pp. MR-1329992
6. Dall'Aglio, P., Leone, C.: Obstacle Problems with Measure Data and Linear Operators. Potential Anal. 17, (2002), 45-64. MR-1906408
7. Dal Maso, G., Murat, F., Orsina, L., Prignet, A.: Renormalized Solutions of Elliptic Equations with General Measure Data. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 28, (1999), 741-808. MR-1760541
8. Fukushima, M., Oshima, Y., Takeda, M.: Dirichlet Forms and Symmetric Markov Processes. Walter de Gruyter, Berlin, 1994. x+489 pp. MR-1303354
9. Kinderlehrer, D., Stampacchia, G.: An introduction to variational inequalities and their applications. Academic Press, New York, 1980. xiv+313 pp. MR-0567696
10. Klimsiak, T.: On time-dependent functionals of diffusions corresponding to divergence form operators. J. Theoret. Probab. DOI 10.1007/s10959-011-0381-4
11. Krasnosel'skii, M.A.: Topological methods in the theory of nonlinear integral equations. Macmillan, New York, 1964. xi+395 pp. MR-0159197
12. Kufner, A., John, O., Fučík, S.: Function spaces. Noordhoff International Publishing Leyden, Academia, Prague, 1977. xv+454 pp. MR-0482102
13. Leone, C.: Existence and uniqueness of solutions for nonlinear obstacle problems with measure data. Nonlinear Anal. Ser. A: Theory Methods 43, (2001), 199-215. MR-1790102
14. 1. Nonlinear Anal. 32, (1998), 325-334. MR-1610574
15. Pardoux, É., Rǎşcanu, A.: Backward stochastic differential equations with subdifferential operator and related variational inequalities. Stochastic Process. Appl. 76, (1998), 191-215. MR-1642656
16. Rozkosz, A.: On Dirichlet Processes Associated with Second Order Divergence Form Operators. Potential Anal. 14, (2001), 123-149. MR-1812438
17. Rozkosz, A.: BSDEs with random terminal time and semilinear elliptic PDEs in divergence form. Studia Math. 170, (2005), 1-21. MR-2142181
18. Rozkosz, A.: On stochastic representation for solutions of the Dirichlet problem for elliptic equations in divergence form. Stoch. Anal. Appl. 27, (2009), 1-15. MR-2473137
19. p solutions of reflected BSDEs under monotonicity condition. arXiv:1205.6737
20. Stroock, D.W.: Diffusion Semigroups Corresponding to Uniformly Elliptic Divergence Form Operators. Lecture Notes in Math. 1321, (1988), 316-347. MR-0960535