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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

A Regularity Result for Quasilinear Stochastic Partial Differential Equations of Parabolic Type

Arnaud Debussche, Sylvain De Moor and Martina Hofmanová


We consider a quasilinear parabolic stochastic partial differential equation driven by a multiplicative noise and study regularity properties of its weak solution satisfying classical a priori estimates. In particular, we determine conditions on coefficients and initial data under which the weak solution is Hölder continuous in time and possesses spatial regularity that is only limited by the regularity of the given data. Our proof is based on an efficient method of increasing regularity: the solution is rewritten as the sum of two processes, one solves a linear parabolic SPDE with the same noise term as the original model problem whereas the other solves a linear parabolic PDE with random coefficients. This way, the required regularity can be achieved by repeatedly making use of known techniques for stochastic convolutions and deterministic PDEs.


Related publications

2015 Repository Open Access
Arnaud Debussche, Sylvain De Moor and Martina Hofmanová

A regularity result for quasilinear stochastic partial differential equations of parabolic type

In: SIAM journal on mathematical analysis, 47 (2015) 2, pp. 1590-1614