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2012 Optimal regularity for semilinear stochastic partial differential equations with multiplicative noise
Raphael Kruse, Stig Larsson
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Electron. J. Probab. 17: 1-19 (2012). DOI: 10.1214/EJP.v17-2240

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.

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Raphael Kruse. Stig Larsson. "Optimal regularity for semilinear stochastic partial differential equations with multiplicative noise." Electron. J. Probab. 17 1 - 19, 2012. https://doi.org/10.1214/EJP.v17-2240

Information

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

zbMATH: 1255.35221
MathSciNet: MR2968672
Digital Object Identifier: 10.1214/EJP.v17-2240

Subjects:
Primary: 35B65
Secondary: 35R60 , 60H15

Keywords: Hölder continuity , linear growth bound , Lipschitz nonlinearities , Multiplicative noise , SPDE , temporal and spatial regularity

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