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

@article{Debussche2014ARR,
  title={A Regularity Result for Quasilinear Stochastic Partial Differential Equations of Parabolic Type},
  author={Arnaud Debussche and Sylvain de Moor and Martina Hofmanov{\'a}},
  journal={SIAM J. Math. Analysis},
  year={2014},
  volume={47},
  pages={1590-1614}
}
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 H\"older 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… CONTINUE READING
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