Marinelli, CarloNualart, EulàliaQuer-Sardanyons, Lluís2021-02-222021-02-222013Marinelli 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/s11118-012-9330-90926-2601http://hdl.handle.net/10230/46561We 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.application/pdfeng© Springer The final publication is available at Springer via http://dx.doi.org/10.1007/s11118-012-9330-9Existence and regularity of the density for solutions to semilinear dissipative parabolic SPDEsinfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1007/s11118-012-9330-9Stochastic partial differential equationExistence and regularity of densitiesMalliavin Calculusinfo:eu-repo/semantics/openAccess