Elliptic equations for measures: Regularity and global bounds of densities

Journal des Mathematiques Pures et Appliquees

Volumn 85, Issue 6, 2006, Pages 743-757

  Bogachev, Vladimir I ^a   Krylov, Nicolai V ^b   Röckner, Michael ^c  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

^b UNIVERSITY OF MINNESOTA   (United States)

^c PURDUE UNIVERSITY   (United States)

Author keywords

Elliptic equations for measures; Elliptic operators; Elliptic regularity; Invariant measures of diffusions; Sobolev spaces

Indexed keywords

EID: 33744917013     PISSN: 00217824     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.matpur.2005.11.006     Document Type: Article

References (18)

1. Albeverio S., Bogachev V.I., and Röckner M. On uniqueness of invariant measures for finite- and infinite-dimensional diffusions. Comm. Pure Appl. Math. 52 (1999) 325-362
2. Bogachev V.I., Krylov N.V., and Röckner M. Regularity of invariant measures: the case of non-constant diffusion part. J. Funct. Anal. 138 (1996) 223-242
3. n. Ann. Scuola Norm. Sup. Pisa 24 (1997) 451-461
4. Bogachev V.I., Krylov N.V., and Röckner M. On regularity of transition probabilities and invariant measures of singular diffusions under minimal conditions. Comm. Partial Differential Equations 26 11-12 (2001) 2037-2080
5. Bogachev V.I., and Röckner M. A generalization of Hasminskii's theorem on existence of invariant measures for locally integrable drifts. Theory Probab. Appl. 45 3 (2000) 363-378
6. Bogachev V.I., and Röckner M. Elliptic equations for measures on infinite dimensional spaces and applications. Probab. Theory Relat. Fields 120 (2001) 445-496
7. Bogachev V.I., and Röckner M. Invariant measures of diffusion processes: regularity, existence, and uniqueness problems. In: Da Prato G., et al. (Ed). Stochastic Partial Differential Equations and Applications (2002), Marcel Dekker, New York 69-87
8. p-uniqueness and essential self-adjointness of symmetric diffusion operators on Riemannian manifolds. Sbornik Math. 194 7 (2003) 15-24
9. V.I. Bogachev, M. Röckner, S.V. Shaposhnikov, Global regularity and bounds for solutions of parabolic equations for probability measures, Theory Probab. Appl., in press
10. Bogachev V.I., Röckner M., and Stannat W. Uniqueness of solutions of elliptic equations and uniqueness of invariant measures of diffusions. Sbornik Math. 193 7 (2002) 945-976
11. Bogachev V.I., Röckner M., and Wang F.-Y. Elliptic equations for invariant measures on finite and infinite dimensional manifolds. J. Math. Pures Appl. 80 (2001) 177-221
12. Bogachev V.I., Röckner M., and Wang F.-Y. Invariance implies Gibbsian: some new results. Comm. Math. Phys. 248 (2004) 335-355
13. Eberle A. Uniqueness and Non-Uniqueness of Singular Diffusion Operators. Lecture Notes in Math vol. 1718 (1999), Springer-Verlag, Berlin
14. Krylov N.V. Lectures on Elliptic and Parabolic Equations in Sobolev Spaces. Topics in PDEs Math. vol. 8590 (2004), Univ. of Minnesota, Minneapolis
15. Lunardi A. Analytic Semigroups and Optimal Regularity in Parabolic Problems (1995), Birkhäuser-Verlag, Basel
16. Lunardi A., and Vespri V. Hölder regularity in variational parabolic nonhomogeneous equations. J. Differential Equations 94 1 (1991) 1-40
17. Metafune G., Pallara D., and Rhandi A. Global regularity of invariant measures. J. Funct. Anal. 223 (2005) 396-424
18. 1: existence, uniqueness and associated Markov processes. Ann. Scuola Norm. Super. Pisa Cl. Sci. (4) 28 1 (1999) 99-140