Preprint of the project:
10-093 Raphael Kruse, Stig Larsson.
Optimal regularity for semilinear stochastic partial differential equations with multiplicative noise
This paper deals with the spatial and
temporal regularity of the unique Hilbert space valued mild
solution to a semilinear stochastic partial differential
equation with nonlinear terms that satisfy global Lipschitz
conditions. It is shown that the mild solution has the same
optimal regularity properties as the stochastic convolution.
The proof is elementary and makes use of existing results on
the regularity of the solution, in particular, the Hölder
continuity with a non-optimal exponent.
