Existence and Regularity of the Density for Solutions to Semilinear Dissipative Parabolic SPDEs

Carlo Marinelli, Eulalia Nualart, Lluís Quer-Sardanyons

Research output: Contribution to journalArticleResearchpeer-review

4 Citations (Scopus)

Abstract

We prove existence and smoothness of the density of the solution to a nonlinear stochastic heat equation on L2(O) (evaluated at fixed points in time and space), where O is an open bounded domain in ℝd with smooth boundary. The equation is driven by an additive Wiener noise and the nonlinear drift term is the superposition operator associated to a real function which is assumed to be (maximal) monotone, continuously differentiable, and growing not faster than a polynomial. The proof uses tools of the Malliavin calculus combined with methods coming from the theory of maximal monotone operators. © 2013 Springer Science+Business Media Dordrecht.
Original languageEnglish
Pages (from-to)287-311
JournalPotential Analysis
Volume39
Issue number3
DOIs
Publication statusPublished - 1 Oct 2013

Keywords

  • Existence and regularity of densities
  • Malliavin Calculus
  • Stochastic partial differential equation

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