# American Institute of Mathematical Sciences

June  2013, 6(3): 637-647. doi: 10.3934/dcdss.2013.6.637

## Schauder estimates for some perturbation of an infinite dimensional Ornstein--Uhlenbeck operator

 1 Scuola Normale Superiore di Pisa, Palazzo della Carovana, Piazza dei Cavalieri, 7, 56126 Pisa, Italy

Received  April 2010 Revised  October 2010 Published  December 2012

We prove some Shauder estimates for an elliptic equation in Hilbert spaces.
Citation: Giuseppe Da Prato. Schauder estimates for some perturbation of an infinite dimensional Ornstein--Uhlenbeck operator. Discrete & Continuous Dynamical Systems - S, 2013, 6 (3) : 637-647. doi: 10.3934/dcdss.2013.6.637
##### References:
 [1] J. M. Bismut, "Large Deviations and the Malliavin Calculus,", Birkhäuser, (1984).   Google Scholar [2] P. Cannarsa and G. Da Prato, Schauder estimates for Kolmogorov equations in Hilbert spaces,, in, 350 (1996), 100.   Google Scholar [3] S. Cerrai, Weakly continuous semigroups in the space of functions with polynomial growth,, Dyn. Syst. Appl., 4 (1995), 351.   Google Scholar [4] G. Da Prato, "Kolmogorov Equations for Stochastic PDEs,", Birkhäuser, (2004).  doi: 10.1007/978-3-0348-7909-5.  Google Scholar [5] G. Da Prato and J. Zabczyk, "Second Order Partial Differential Equations in Hilbert spaces,", London Mathematical Society Lecture Notes, 293 (2002).  doi: 10.1017/CBO9780511543210.  Google Scholar [6] K. D. Elworthy, Stochastic flows on Riemannian manifolds,, in, II (1992), 33.  doi: 10.1007/978-1-4612-0389-6.  Google Scholar [7] A. Lunardi, An interpolation method to characterize domains of generators of semigroups,, Semigroup Forum, 53 (1996), 321.  doi: 10.1007/BF02574147.  Google Scholar [8] E. Priola, On a class of Markov type semigroups in spaces of uniformly continuous and bounded functions,, Studia Math., 136 (1995), 271.   Google Scholar [9] H. Triebel, "Interpolation Theory, Function Spaces, Differential Operators,", North-Holland, (1978).   Google Scholar

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##### References:
 [1] J. M. Bismut, "Large Deviations and the Malliavin Calculus,", Birkhäuser, (1984).   Google Scholar [2] P. Cannarsa and G. Da Prato, Schauder estimates for Kolmogorov equations in Hilbert spaces,, in, 350 (1996), 100.   Google Scholar [3] S. Cerrai, Weakly continuous semigroups in the space of functions with polynomial growth,, Dyn. Syst. Appl., 4 (1995), 351.   Google Scholar [4] G. Da Prato, "Kolmogorov Equations for Stochastic PDEs,", Birkhäuser, (2004).  doi: 10.1007/978-3-0348-7909-5.  Google Scholar [5] G. Da Prato and J. Zabczyk, "Second Order Partial Differential Equations in Hilbert spaces,", London Mathematical Society Lecture Notes, 293 (2002).  doi: 10.1017/CBO9780511543210.  Google Scholar [6] K. D. Elworthy, Stochastic flows on Riemannian manifolds,, in, II (1992), 33.  doi: 10.1007/978-1-4612-0389-6.  Google Scholar [7] A. Lunardi, An interpolation method to characterize domains of generators of semigroups,, Semigroup Forum, 53 (1996), 321.  doi: 10.1007/BF02574147.  Google Scholar [8] E. Priola, On a class of Markov type semigroups in spaces of uniformly continuous and bounded functions,, Studia Math., 136 (1995), 271.   Google Scholar [9] H. Triebel, "Interpolation Theory, Function Spaces, Differential Operators,", North-Holland, (1978).   Google Scholar
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