Electronic Journal of Probability

Optimal regularity for semilinear stochastic partial differential equations with multiplicative noise

Raphael Kruse and Stig Larsson

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35B65: Smoothness and regularity of solutions
Secondary: 35R60: Partial differential equations with randomness, stochastic partial differential equations [See also 60H15] 60H15: Stochastic partial differential equations [See also 35R60]

SPDE Hölder continuity temporal and spatial regularity multiplicative noise Lipschitz nonlinearities linear growth bound

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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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