Irregular semi-convex gradient systems perturbed by noise and application to the stochastic Cahn-Hilliard equation
Annales de l'I.H.P. Probabilités et statistiques, Tome 40 (2004) no. 1, pp. 73-88.
@article{AIHPB_2004__40_1_73_0,
     author = {Da Prato, Giuseppe and Debussche, Arnaud and Tubaro, Luciano},
     title = {Irregular semi-convex gradient systems perturbed by noise and application to the stochastic {Cahn-Hilliard} equation},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {73--88},
     publisher = {Elsevier},
     volume = {40},
     number = {1},
     year = {2004},
     doi = {10.1016/j.anihpb.2003.06.003},
     zbl = {1038.60055},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.anihpb.2003.06.003/}
}
TY  - JOUR
AU  - Da Prato, Giuseppe
AU  - Debussche, Arnaud
AU  - Tubaro, Luciano
TI  - Irregular semi-convex gradient systems perturbed by noise and application to the stochastic Cahn-Hilliard equation
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 2004
SP  - 73
EP  - 88
VL  - 40
IS  - 1
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.1016/j.anihpb.2003.06.003/
DO  - 10.1016/j.anihpb.2003.06.003
LA  - en
ID  - AIHPB_2004__40_1_73_0
ER  - 
%0 Journal Article
%A Da Prato, Giuseppe
%A Debussche, Arnaud
%A Tubaro, Luciano
%T Irregular semi-convex gradient systems perturbed by noise and application to the stochastic Cahn-Hilliard equation
%J Annales de l'I.H.P. Probabilités et statistiques
%D 2004
%P 73-88
%V 40
%N 1
%I Elsevier
%U http://archive.numdam.org/articles/10.1016/j.anihpb.2003.06.003/
%R 10.1016/j.anihpb.2003.06.003
%G en
%F AIHPB_2004__40_1_73_0
Da Prato, Giuseppe; Debussche, Arnaud; Tubaro, Luciano. Irregular semi-convex gradient systems perturbed by noise and application to the stochastic Cahn-Hilliard equation. Annales de l'I.H.P. Probabilités et statistiques, Tome 40 (2004) no. 1, pp. 73-88. doi : 10.1016/j.anihpb.2003.06.003. http://archive.numdam.org/articles/10.1016/j.anihpb.2003.06.003/

[1] S. Albeverio, R. Høegh-Krohn, Dirichlet forms and diffusion processes on rigged Hilbert spaces, Z. Wahrsch. Geb. 40 (1977) 1-57. | MR | Zbl

[2] S. Albeverio, V. Kondratiev, M. Röckner, Dirichlet operators via stochastic analysis, J. Funct. Anal. 128 (1) (1995) 102-138. | MR | Zbl

[3] D. Bakry, L'hypercontractivité et son utilisation en théorie des semi-groupes, Lectures on Probability Theory, Lecture Notes in Math., vol. 1581, Springer, 1994. | MR | Zbl

[4] D. Blömker, S. Majer-Paape, T. Wanner, Spinodal decomposition for the Cahn-Hilliard-Cook equation, Comm. Math. Phys. 223 (2001) 553-582. | Zbl

[5] A. Chojnowska-Michalik, B. Goldys, On regularity properties of nonsymmetric Ornstein-Uhlenbeck semigroup in Lp spaces, Stoch. Stoch. Reports 59 (1996) 183-209. | Zbl

[6] C. Cardon-Weber, Cahn-Hilliard stochastic equations: strict positivity of the density, Stochastic and Stochastic Reports 72 (2002) 191-277. | Zbl

[7] G. Da Prato, A. Debussche, Stochastic Cahn-Hilliard equation, Nonlinear Anal. 26 (2) (1996) 241-263. | Zbl

[8] G. Da Prato, A. Debussche, B. Goldys, Some properties of invariant measures of nonsymmetric dissipative stochastic systems, Probab. Theory Related Fields 123 (3) (2002) 355-380. | MR | Zbl

[9] G. Da Prato, L. Tubaro, Some results about dissipativity of Kolmogorov operators, Czechoslovak Math. J. 51 (4) (2001) 685-699. | MR | Zbl

[10] G. Da Prato, L. Tubaro, On a class of gradient systems with irregular potentials, in: Infinite Dimensional Analysis, Quantum Probability and Related Topics, vol. 4, 2001, pp. 183-194. | MR | Zbl

[11] G. Da Prato, J. Zabczyk, Ergodicity for Infinite Dimensional Systems, London Mathematical Society Lecture Notes, vol. 229, Cambridge University Press, 1996. | MR | Zbl

[12] G. Da Prato, J. Zabczyk, Second Order Partial Differential Equations in Hilbert Spaces, London Mathematical Society Lecture Notes, vol. 293, Cambridge University Press, 2002. | MR | Zbl

[13] A. Eberle, Uniqueness and Non-Uniqueness of Singular Diffusion Operators, Lecture Notes in Mathematics, vol. 1718, Springer-Verlag, 1999. | MR | Zbl

[14] V. Liskevich, M. Röckner, Strong uniqueness for a class of infinite dimensional Dirichlet operators and application to stochastic quantization, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 27 (1999) 69-91. | Numdam | MR | Zbl

[15] G. Lumer, R.S. Phillips, Dissipative operators in a Banach space, Pacific J. Math. 11 (1961) 679-698. | MR | Zbl

Cité par Sources :