For a class of stochastic partial differential equations studied by Conus and Dalang, we prove the existence of density of the probability law of the solution at a given point $(t,x)$, and that the density belongs to some Besov space. The proof relies on a method developed by Debussche and Romito.The result can be applied to the solution of the stochastic wave equation with multiplicative noise, Lipschitz coefficients and any spatial dimension $d\ge 1$, and also to the heat equation.This provides an extension of earlier results.
"Absolute continuity for SPDEs with irregular fundamental solution." Electron. Commun. Probab. 20 1 - 11, 2015. https://doi.org/10.1214/ECP.v20-3831