Optimal Regularity for Semilinear Stochastic Partial Differential Equations with Multiplicative Noise

Details Optimal Regularity for Semilinear Stochastic Partial Differential Equations with Multiplicative Noise Optimal Regularity for Semilinear Stochastic Partial Differential Equations with Multiplicative Noise

2011-09-29

arxiv.org/abs/1109.6487v1

Mathematics

Analysis of PDEs

Scientific paper

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 H\"older continuity with a non-optimal exponent.

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