Abstract
We prove maximal dissipativity of some gradient systems having a convex potential.
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References
S. Albeverio and R. Hoegh-Krohn, Dirichlet forms and diffusion processes on rigged Hilbert spaces, Z. Wahrsch. verw. Geb. 40 (1977), 1–57.
S. Albeverio, V. Kondratiev and M. Röckner, Dirichlet operators via stochastic analysis, J. Funct. Analysis, 128 (1995), 102–138.
Yu. M. Berezanskii, Self-adjoint operators in spaces of functions of infinitely many variables, Transl. Math. Monography, Vol. 63, Amer. Mat. Soc. Providence RI, 1986.
V. Barbu, Nonlinear semigroups and differential equations in Banach spaces, Noordhoff, 1976.
V. Barbu and A. RascanuParabolic variational inequalities with singular inputs, Differential Integral equations, 10 (1997), 67–87.
A. Bensoussan and A. RascanuStochastic variational equations in infinite dimensional spaces, Numer. Funct. Anal. Optimiz., 18 (1997), 19–54.
J. M. Bismut, Large Deviations and the Malliavin Calculus, Birkhäuser, 1984.
E. Cepa, Multivalued stochastic differential equations, C.R. Acad. Sci. Paris, Ser 1, Math., 319 (1994), 1075–1078.
G. Da PratoApplications croissantes et équations d’évolutions dans les espaces de Banach, Academic Press, 1976.
G. Da Prato, Regularity results for Kolmogorov equations on L 2 (H, µ) spaces and applications, Ukrainian Mathematical Journal, m. 49 (1997), 448–457.
G. Da PratoThe Ornstein-Uhlenbeck generator perturbed by the gradient of a potential, Bollettino UMI, (8) I-B, 501–519, 1998.
G. Da Prato and B. Goldys, Invariant measures of non symmetric dissipative stochastic systems, Preprint Scuola Normale Superiore di Pisa, 1999.
G. Da Prato and L. Tubaro, A new method to prove self-adjointness of some infinite dimensional Dirichlet operator, Probab. Theory Relat. Fields, 118 (2000), 131–145.
G. Da Prato and J. Zabczyk, Ergodicity for Infinite Dimensional Systems, London Mathematical Society Lecture Notes, n.229, Cambridge University Press, 1996.
J. Dohmann, Strong Feller properties and path regularity of Markov processes, Diploma Thesis, University of Bielefeld, 2001.
K. D. Elworthy, Stochastic flows on Riemannian manifolds. In M.A. Pinsky and V. Wihstutz, editors, Diffusion processes and related problems in analysis, Vol. II, 33–72, Birkhäuser, 1992.
U. G. Haussman and E. Pardoux, Stochastic variational inequalities of parabolic type, Appl. Math. Optimiz., 20 (1989), 163–192.
V. Liskevich and M. Röckner, Strong uniqueness for a class of infinite dimensional Dirichlet operators and application to stochastic quantization, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 27 (1999), 69–91.
H. Long and I. Simao, Kolmogorov equations in Hilbert spaces with application to essential self-adjointness of symmetric diffusion operators, Osaka Journal of Mathematics, (to appear).
G. Lumer and R. S. Phillips, Dissipative operators in a Banach space, Pacific J. Math, 11 (1961), 679–698.
Z. M. Ma and M. Röckner, Introduction to the Theory of (Non Symmetric) Dirichlet Forms, Springer-Verlag, 1992.
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Da Prato, G. (2002). Monotone Gradient Systems in L 2 Spaces. In: Dalang, R.C., Dozzi, M., Russo, F. (eds) Seminar on Stochastic Analysis, Random Fields and Applications III. Progress in Probability, vol 52. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8209-5_6
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DOI: https://doi.org/10.1007/978-3-0348-8209-5_6
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