Sub-gaussian measures and  associated semilinear problems

Fougères, Pierre; Roberto, Cyril; Zegarliński, Boguslaw

doi:10.4171/rmi/679

Revista Matemática Iberoamericana

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Volume 28, Issue 2, 2012, pp. 305–350

DOI: 10.4171/rmi/679

Sub-gaussian measures and associated semilinear problems

Pierre Fougères (1), Cyril Roberto (2) and Boguslaw Zegarliński (3)

(1) Institut de Mathématiques de Toulouse, Université Paul Sabatier, 118 route de Narbonne, 31062, TOULOUSE CEDEX 9, FRANCE
(2) Laboratoire d'Analyse et de Mathématiques Appliqué, Université de Marne-la-Vallée, 5, bd Descartes, 77454, MARNE LA VALLÉE CEDEX 2, FRANCE
(3) Department of Mathematics, Imperial College, 180 Queen's Gate, SW7 2BZ, LONDON, UNITED KINGDOM

We study the existence, smoothing properties and the long time behaviour for a class of nonlinear Cauchy problems in infinite dimensions under the assumption of $F$-Sobolev inequalities.

Keywords: $F$-Sobolev inequalities, semilinear parabolic problems, infinite dimensions