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 and 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.

[2]

P. Cannarsa and G. Da Prato, Schauder estimates for Kolmogorov equations in Hilbert spaces, in "Progress in Elliptic and Parabolic Partial Differential Equations" (eds. A. Alvino, P. Buonocore, V. Ferone, E. Giarrusso, S. Matarasso, R. Toscano and G. Trombetti), Research Notes in Mathematics 350, Pitman, (1996), 100-111. in "Contributions to Nonlinear Functional Analysis" (eds. E.H. Zarantonello and Author 2), Academic Press, (1971), 33-75. Discrete Continuous Dynam. Systems - B, 4 (2004), 1065-1089.

[3]

S. Cerrai, Weakly continuous semigroups in the space of functions with polynomial growth, Dyn. Syst. Appl., 4 (1995), 351-372.

[4]

G. Da Prato, "Kolmogorov Equations for Stochastic PDEs," Birkhäuser, 2004. doi: 10.1007/978-3-0348-7909-5.

[5]

G. Da Prato and J. Zabczyk, "Second Order Partial Differential Equations in Hilbert spaces," London Mathematical Society Lecture Notes, 293, Cambridge University Press, 2002. doi: 10.1017/CBO9780511543210.

[6]

K. D. Elworthy, Stochastic flows on Riemannian manifolds, in "Diffusion Processes and Related Problems in Analysis" II, (eds. M. A. Pinsky and V. Wihstutz), Birkhäuser, (1992), 33-72. doi: 10.1007/978-1-4612-0389-6.

[7]

A. Lunardi, An interpolation method to characterize domains of generators of semigroups, Semigroup Forum, 53 (1996), 321-329. doi: 10.1007/BF02574147.

[8]

E. Priola, On a class of Markov type semigroups in spaces of uniformly continuous and bounded functions, Studia Math., 136 (1995), 271-295.

[9]

H. Triebel, "Interpolation Theory, Function Spaces, Differential Operators," North-Holland, 1978.

show all references

References:
[1]

J. M. Bismut, "Large Deviations and the Malliavin Calculus," Birkhäuser, 1984.

[2]

P. Cannarsa and G. Da Prato, Schauder estimates for Kolmogorov equations in Hilbert spaces, in "Progress in Elliptic and Parabolic Partial Differential Equations" (eds. A. Alvino, P. Buonocore, V. Ferone, E. Giarrusso, S. Matarasso, R. Toscano and G. Trombetti), Research Notes in Mathematics 350, Pitman, (1996), 100-111. in "Contributions to Nonlinear Functional Analysis" (eds. E.H. Zarantonello and Author 2), Academic Press, (1971), 33-75. Discrete Continuous Dynam. Systems - B, 4 (2004), 1065-1089.

[3]

S. Cerrai, Weakly continuous semigroups in the space of functions with polynomial growth, Dyn. Syst. Appl., 4 (1995), 351-372.

[4]

G. Da Prato, "Kolmogorov Equations for Stochastic PDEs," Birkhäuser, 2004. doi: 10.1007/978-3-0348-7909-5.

[5]

G. Da Prato and J. Zabczyk, "Second Order Partial Differential Equations in Hilbert spaces," London Mathematical Society Lecture Notes, 293, Cambridge University Press, 2002. doi: 10.1017/CBO9780511543210.

[6]

K. D. Elworthy, Stochastic flows on Riemannian manifolds, in "Diffusion Processes and Related Problems in Analysis" II, (eds. M. A. Pinsky and V. Wihstutz), Birkhäuser, (1992), 33-72. doi: 10.1007/978-1-4612-0389-6.

[7]

A. Lunardi, An interpolation method to characterize domains of generators of semigroups, Semigroup Forum, 53 (1996), 321-329. doi: 10.1007/BF02574147.

[8]

E. Priola, On a class of Markov type semigroups in spaces of uniformly continuous and bounded functions, Studia Math., 136 (1995), 271-295.

[9]

H. Triebel, "Interpolation Theory, Function Spaces, Differential Operators," North-Holland, 1978.

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