Optimal regularity for semilinear stochastic partial differential equations with multiplicative noise
Journal article, 2012

This paper deals with the spatial and temporal regularity of the unique Hilbert space valued mild solution to a semilinear stochastic parabolic partial differential equation with nonlinear terms that satisfy global Lipschitz conditions and certain linear growth bounds. 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.


multiplicative noise

temporal and spatial regularity

Hölder continuity

Lipschitz nonlinearities


Raphael Kruse

Stig Larsson

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Electronic Journal of Probability

1083-6489 (ISSN)

Vol. 17 artikel nr 65-


Basic sciences

Subject Categories

Probability Theory and Statistics



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