Fokker-Planck equations and maximal dissipativity for Kolmogorov operators with time dependent singular drifts in Hilbert spaces

Journal of Functional Analysis

Volumn 256, Issue 4, 2009, Pages 1269-1298

  Bogachev, V I ^a   Da Prato, G ^b   Rockner M ^c,d  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

^b SCUOLA NORMALE SUPERIORE   (Italy)

^c BIELEFELD UNIVERSITY   (Germany)

^d PURDUE UNIVERSITY   (United States)

Author keywords

Fokker Planck equations; Kolmogorov operators; Maximal dissipativity; Parabolic equations for measures; Singular coefficients; Stochastic PDEs

Indexed keywords

EID: 58149348709     PISSN: 00221236     EISSN: 10960783     Source Type: Journal    
DOI: 10.1016/j.jfa.2008.05.005     Document Type: Article

References (20)

1. Bogachev V., Da Prato G., and Röckner M. Existence of solutions to weak parabolic equations for measures. Proc. London Math. Soc. (3) 88 (2004) 753-774
2. Bogachev V., Da Prato G., Röckner M., and Stannat W. Uniqueness of solutions to weak parabolic equations for measures. Bull. London Math. Soc. 39 (2007) 631-640
3. Bogachev V., Da Prato G., and Röckner M. On parabolic equations for measures. Comm. Partial Differential Equations 33 3 (2008) 397-418
4. Bogachev V., Da Prato G., and Röckner M. Infinite dimensional Kolmogorov operators with time dependent drift coefficients. Dokl. Ross. Akad. Nauk 419 5 (2008) 587-591 (in Russian); English transl.: in:
5. Bogachev V., Da Prato G., and Röckner M. Infinite dimensional Kolmogorov operators with time dependent drift coefficients. Dokl. Akad. Nauk 77 2 (2008) 276-280
6. V. Bogachev, G. Da Prato, M. Röckner, Parabolic equations for measures on infinite-dimensional spaces, Dokl. Math. (2008), in press
7. Cerrai S. Weakly continuous semigroups in the space of functions with polynomial growth. Dynam. Syst. Appl. 4 (1995) 351-372
8. Cerrai S. Second Order PDE's in Finite and Infinite Dimensions. A Probabilistic Approach. Lecture Notes in Math. vol. 1762 (2001), Springer-Verlag
9. Da Prato G. Kolmogorov Equations for Stochastic PDEs (2004), Birkhäuser
10. Da Prato G. Introduction to Stochastic Analysis and Malliavin Calculus. Publ. Sc. Norm. Sup. vol. 6 (2007), Birkhäuser
11. Da Prato G., and Röckner M. Singular dissipative stochastic equations in Hilbert spaces. Probab. Theory Related Fields 124 (2002) 261-303
12. Da Prato G., and Röckner M. Dissipative stochastic equations in Hilbert space with time dependent coefficients. Atti Accad. Naz. Lincei 17 (2006) 397-403
13. Da Prato G., and Röckner M. A note on evolution systems of measures for time-dependent stochastic differential equations. Progr. Probab. vol. 59 (2007), Birkhäuser 115-122
14. Da Prato G., and Tubaro L. Some results about dissipativity of Kolmogorov operators. Czechoslovak Math. J. 51 (2001) 685-699
15. Da Prato G., and Zabczyk J. Stochastic Equations in Infinite Dimensions (1992), Cambridge Univ. Press
16. Da Prato G., and Zabczyk J. Ergodicity for Infinite Dimensional Systems. London Math. Soc. Lecture Note Ser. vol. 229 (1996), Cambridge Univ. Press
17. Da Prato G., and Zabczyk J. Second Order Partial Differential Equations in Hilbert Spaces. London Math. Soc. Lecture Note Ser. vol. 293 (2002), Cambridge Univ. Press
18. Eberle A. Uniqueness and Non-uniqueness of Semigroups Generated by Singular Diffusion Operators. Lecture Notes in Math. vol. 1718 (1999), Springer-Verlag
19. Pazy A. Semigroups of Linear Operators and Applications to Partial Differential Equations (1983), Springer-Verlag
20. Priola E. On a class of Markov type semigroups in spaces of uniformly continuous and bounded functions. Studia Math. 136 (1999) 271-295