Existence and regularity of the density for solutions to semilinear dissipative parabolic SPDEs

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  • dc.contributor.author Marinelli, Carlo
  • dc.contributor.author Nualart, Eulàlia
  • dc.contributor.author Quer-Sardanyons, Lluís
  • dc.date.accessioned 2021-02-22T08:57:06Z
  • dc.date.available 2021-02-22T08:57:06Z
  • dc.date.issued 2013
  • dc.description.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.en
  • dc.description.sponsorship Part of the work for this paper was carried out while the authors were visiting the Hausdorff Institute for Mathematics in Bonn, whose hospitality and financial support are gratefully acknowledged. L. Quer-Sardanyons is also supported by the grant MICINNFEDER Ref. MTM2009-08869.
  • dc.format.mimetype application/pdf
  • dc.identifier.citation Marinelli C, Nualart E, Quer-Sardanyons L. Existence and regularity of the density for solutions to semilinear dissipative parabolic SPDEs. Potential Anal. 2013 Jan 25;39(3):287–311. DOI: 10.1007/s11118-012-9330-9
  • dc.identifier.doi http://dx.doi.org/10.1007/s11118-012-9330-9
  • dc.identifier.issn 0926-2601
  • dc.identifier.uri http://hdl.handle.net/10230/46561
  • dc.language.iso eng
  • dc.publisher Springer
  • dc.relation.ispartof Potential Analysis. 2013 Jan 25;39(3):287–311
  • dc.relation.projectID info:eu-repo/grantAgreement/ES/3PN/MTM2009-08869
  • dc.rights © Springer The final publication is available at Springer via http://dx.doi.org/10.1007/s11118-012-9330-9
  • dc.rights.accessRights info:eu-repo/semantics/openAccess
  • dc.subject.keyword Stochastic partial differential equationen
  • dc.subject.keyword Existence and regularity of densitiesen
  • dc.subject.keyword Malliavin Calculusen
  • dc.title Existence and regularity of the density for solutions to semilinear dissipative parabolic SPDEsen
  • dc.type info:eu-repo/semantics/article
  • dc.type.version info:eu-repo/semantics/acceptedVersion

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