Stochastic variational inequalities and regularity for degenerate stochastic partial differential equations
- Authors: Benjamin Gess, Michael Röckner
- Preprint year: 2014
- First public date: 2014-05-22
- arXiv: 1405.5866
- Status: Published
- Publication type: Journal article
- Publication year: 2017
- Journal: Transactions of the American Mathematical Society, 369 (2017) 5, pp. 3017-3045
- DOI: 10.1090/tran/6981
Abstract
The regularity and characterization of solutions to degenerate, quasilinear SPDE is studied. Our results are two-fold: First, we prove regularity results for solutions to certain degenerate, quasilinear SPDE driven by Lipschitz continuous noise. In particular, this provides a characterization of solutions to such SPDE in terms of (generalized) strong solutions. Second, for the one-dimensional stochastic mean curvature flow with normal noise we adapt the notion of stochastic variational inequalities to provide a characterization of solutions previously obtained in a limiting sense only. This solves a problem left open in [Es-Sarhir, von Renesse; SIAM, 2012] and sharpens regularity properties obtained in [Es-Sarhir, von Renesse, Stannat; NoDEA, 2012].