Absolute Continuity of Solutions to Reaction-Diffusion Equations with Multiplicative Noise

Carlo Marinelli*, Lluís Quer-Sardanyons

*Corresponding author for this work

Research output: Contribution to journalArticleResearchpeer-review


We prove absolute continuity of the law of the solution, evaluated at fixed points in time and space, to a parabolic dissipative stochastic PDE on L2(G), where G is an open bounded domain in ℝd with smooth boundary. The equation is driven by a multiplicative Wiener noise and the nonlinear drift term is the superposition operator associated to a real function that is assumed to be monotone, locally Lipschitz continuous, and growing not faster than a polynomial. The proof, which uses arguments of the Malliavin calculus, crucially relies on the well-posedness theory in the mild sense for stochastic evolution equations in Banach spaces.

Original languageEnglish
Pages (from-to)243-261
Number of pages19
JournalPotential Analysis
Issue number2
Publication statusPublished - Aug 2022


  • Malliavin calculus
  • Reaction-diffusion equations
  • Stochastic PDEs

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