Dirichlet problem for parabolic equations on Hilbert spaces

Studia Mathematica

Volumn 141, Issue 2, 2000, Pages 109-142

  Talarczyk, Anna ^a  

^a UNIVERSITY OF WARSAW   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0005519979     PISSN: 00393223     EISSN: None     Source Type: Journal    
DOI: 10.4064/sm-141-2-109-142     Document Type: Article

References (24)

1. R. M. Blumenthal and R. K. Getoor, Markov Processes and Potential Theory, Academic Press, 1968.
2. P. Cannarsa and G. Da Prato, A semigroup approach to Kolmogoroff equations in Hilbert spaces, Appl. Math. Lett. 4 (1991), 49-52.
3. _, _, On functional analysis approach to parabolic equations in infinite dimensions, J. Funct. Anal. 118 (1993), 22-42.
4. Yu. Daleckij, Differential equations with functional derivatives and stochastic equations for generalized random processes, Dokl. Akad. Nauk SSSR 166 (1966), 1035-1038 (in Russian).
5. G. Da Prato, Parabolic Equations in Hilbert Spaces, Scuola Normale Superiore Pisa, Lecture Notes, May 1996.
6. _, Some results on parabolic evolution equations with infinitely many variables, J. Differential Equations 68 (1987), 281-297.
7. _, Stochastic Evolution Equations by Semigroups Methods, Centre De Recerca Matematica, Barcelona, Quaderns 11 (1998).
8. G. Da Prato, B. Gołdys and J. Zabczyk, Ornstein-Uhlenbeck semigroups in open sets of Hilbert spaces, C. R. Acad. Sci. Paris Sér. I 325 (1997), 433-438.
9. G. Da Prato and J. Zabczyk, Smoothing properties of transition semigroups in Hilbert Spaces, Stochastics Stochastics Rep. 35 (1991), 63-77.
10. _, _, Stochastic Equations in Infinite Dimensions, Encyclopedia Math. Appl. 44, Cambridge Univ. Press, 1992.
11. E. B. Davies, One-Parameter Semigroups, Academic Press, 1980.
12. E. B. Dynkin, Markov Processes, Springer, 1965.
13. A. Friedman, Stochastic Differential Equations and Applications, Academic Press, New York, 1975.
14. L. Gross, Potential theory on Hilbert space, J. Funct. Anal. 1 (1967), 123-181.
15. H. H. Kuo, Gaussian Measures in Banach Spaces, Lecture Notes in Math. 463, Springer, Berlin, 1975.
16. H. H. Kuo and M. A. Piech, Stochastic integrals and parabolic equations in abstract Wiener space, Bull. Amer. Math. Soc. 79 (1973), 478-482.
17. n, Studia Math. 128 (1998), 171-198.
18. M. A. Piech, A fundamental solution of the parabolic equation on Hilbert space, J. Funct. Anal. 3 (1969), 85-114.
19. E. Priola, Maximal regularity results for a homogeneous Dirichlet problem in a general half space of a Hilbert space, preprint, Scuola Normale Superiore di Pisa.
20. 2 Euclidean (Quantum) Field Theory, Princeton Univ. Press, 1974.
21. D. W. Stroock, Probability Theory, an Analytic View, Cambridge Univ. Press, 1993.
22. J. Zabczyk, Infinite dimensional diffusions in modeling and analysis, Jahresber. Deutsch. Math.-Verein. 101 (1999), 47-59.
23. _, Parabolic Equations on Hilbert Spaces, Lecture Notes in Math. 1715, Springer, 1999.
24. J. Zabczyk, Stopping problems on Polish spaces, Ann. Univ. Mariae Curie-Skłodowska 51 (1997), 181-199.