## Electronic Journal of Probability

### Optimal regularity for semilinear stochastic partial differential equations with multiplicative noise

#### Abstract

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.

#### Article information

Source
Electron. J. Probab., Volume 17 (2012), paper no. 65, 19 pp.

Dates
Accepted: 18 August 2012
First available in Project Euclid: 4 June 2016

https://projecteuclid.org/euclid.ejp/1465062387

Digital Object Identifier
doi:10.1214/EJP.v17-2240

Mathematical Reviews number (MathSciNet)
MR2968672

Zentralblatt MATH identifier
1255.35221

Rights

#### Citation

Kruse, Raphael; Larsson, Stig. Optimal regularity for semilinear stochastic partial differential equations with multiplicative noise. Electron. J. Probab. 17 (2012), paper no. 65, 19 pp. doi:10.1214/EJP.v17-2240. https://projecteuclid.org/euclid.ejp/1465062387

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