Abstract
In this paper we prove that the density of the solution of a white-noise-driven parabolic stochastic partial differential equation (SPDE) satisfying a strong ellipticity condition is Lipschitz continuous with respect to (w.r.t.) and Lipschitz continuous w.r.t. for all . In addition, we show that it belongs to the Besov space w.r.t. . The proof is based on the Malliavin calculus of variations and on some refined estimates for the Green kernel associated with the SPDE.
Citation
Pierre-Luc Morien. "The Hölder and the Besov regularity of the density for the solution of a parabolic stochastic partial differential equation." Bernoulli 5 (2) 275 - 298, april 1999.
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