Optimal regularity for semilinear stochastic partial differential equations with multiplicative noise
Artikel i vetenskaplig tidskrift, 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.

SPDE

multiplicative noise

temporal and spatial regularity

Hölder continuity

Lipschitz nonlinearities

Författare

Raphael Kruse

Stig Larsson

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

Electronic Journal of Probability

1083-6489 (ISSN)

Vol. 17 artikel nr 65-

Fundament

Grundläggande vetenskaper

Ämneskategorier

Sannolikhetsteori och statistik

DOI

10.1214/EJP.v17-2240

Mer information

Skapat

2017-10-08