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

@article{Debussche2015ARR,
  title={A Regularity Result for Quasilinear Stochastic Partial Differential Equations of Parabolic Type},
  author={A. Debussche and Sylvain de Moor and M. Hofmanov{\'a}},
  journal={SIAM J. Math. Anal.},
  year={2015},
  volume={47},
  pages={1590-1614}
}
  • A. Debussche, Sylvain de Moor, M. Hofmanová
  • Published 2015
  • Mathematics, Computer Science
  • SIAM J. Math. Anal.
  • We consider a nondegenerate quasilinear parabolic stochastic partial differential equation (SPDE) with a uniformly elliptic diffusion matrix. It is driven by a nonlinear noise. We 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 Holder continuous in time and possesses spatial regularity. Our proof is based on an efficient method of increasing… CONTINUE READING
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