Elliptic operators on ℝd with unbounded coefficients

Journal of Differential Equations

Volumn 172, Issue 2, 2001, Pages 333-358

  Da Prato, Giuseppe ^a   Goldys, Beniamin ^b  

^a SCUOLA NORMALE SUPERIORE   (Italy)

^b UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035918654     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.2000.3866     Document Type: Article

References (28)

1. H. Amann, Dual semigroups and second order linear elliptic boundary value problems, Israel J. Math. 45 (1983), 225-254.
2. P. Besala, On the existence of a fundamental solution for a parabolic equation with unbounded coefficients, Ann. Polon. Math. 29 (1975), 403-409.
3. J. M. Bismut, "Large Deviations and the Malliavin Calculus," Birkhäuser, Basel, 1984.
4. V. I. Bogachev, N. V. Krylov, and M. Röckner, On regularity of transition probabilities and invariant measures of singular diffusions under minimal conditions, J. Funct. Anal. 133 (1995), 168-223.
5. V. I. Bogachev and M. Röckner, Regularity of invariant measures on finite and infinite dimensional spaces and applications, J. Funct. Anal. 133 (1995), 168-223.
6. P. Cannarsa and V. Vespri, Generation of analytic semigroups by elliptic operators with unbounded coefficients, SIAM J. Math. Anal. 18 (1985), 857-872.
7. n with coefficients having polynomial growth, Comm. Partial Differential Equations 21 (1996), 281-317.
8. S. Cerrai, Invariant measures for a class of SDE's with drift term having polynomial growth, Dynam. Systems Appl. 5 (1996), 353-370.
9. 2(μ) spaces, Rend. Mat. Acc. Lincei 8 (1997), 101-105.
10. G. Da Prato and J. Zabczyk, "Stochastic Equations in Infinite Dimensions," Cambridge University Press, Cambridge, UK, 1992.
11. G. Da Prato and J. Zabczyk, "Ergodicity for infinite dimensional systems," London Mathematical Society Lecture Notes, Vol. 229, Cambridge Univ. Press, Cambridge, UK, 1966.
12. A. Eberle, "Uniqueness and non-uniqueness of semigroups generated by singular diffusion operators," Lecture Notes in Mathematics, Vol. 1718, Springer-Verlag, Berlin, 1999.
13. J. D. Deuschel and D. Stroock, "Large Deviations," Academic Press, San Diego, 1984.
14. K. D. Elworthy, Stochastic flows on Riemannian manifolds, in "Diffusion Processes and Related Problems in Analysis" (M. A. Pinsky and V. Wihstutz, Eds.), Vol. II, pp. 33-72, Birkhäuser, Basel, 1992.
15. A. Friedman, "Partial Differential Equations of Parabolic Type," Prentice-Hall, Englewood Cliffs, NJ, 1964.
16. L. Gross, Logarithmic Sobolev inequalities, Amer. J. Math. 97 (1976), 1061-1083.
17. S. Ito, Fundamental solutions of parabolic differential equations and boundary value problems, Japan J. Math. 27 (1957), 5-102.
18. O. A. Ladyzhenskaja, V. A. Solonnikov, and N. N. Ural'ceva, "Linear and quasi linear equations of parabolic type," Transl. Math. Monographs, Amer. Math. Soc., Providence, RI, 1968.
19. n, Studia Math. 128 (1998), 171-198.
20. N. V. Krylov, "Introduction to the Theory of Diffusion Processes," Vol. 142, Amer. Math. Soc., Providence, RI, 1991.
21. Z. M. Ma and M. Röckner, "Introduction to the Theory of (Non Symmetric) Dirichlet Forms," Springer-Verlag, Berlin/New York, 1992.
22. A. Pazy, "Semigroups of linear operators and applications to partial differential equations," Applied Mathematical Sciences, Vol. 44, Springer-Verlag, Berlin/New York, 1983.
23. S. Peszat, Compactness of Imbeddings of Some Sobolev Spaces, Warwick Preprints 48/1993.
24. M. Reed and B. Simon, "Methods of Modern Mathematical Physics," Vol. IV, Academic Press, San Diego, 1978.
25. O. Rothaus, Logarithmic Sobolev inequalities and the spectrum of Schrödinger operators, J. Funct. Anal. 42 (1981), 110-120.
26. J. Seidler, Ergodic behaviour of stochastic parabolic equations, Czech. Math. J. 47 (1997), 277-316.
27. 1: Existence, uniqueness and associated Markov processes, Ann. Scuola Norm. Sup. Pisa, Cl. Sci. (4) XXVIII (1999), 99-140.
28. L. Stettner, Remarks on ergodic conditions for Markov processes on polish spaces, Bull. Polish Acad. Sci. 42 (1994), 103-114.