Strong Solutions for Stochastic Partial Differential Equations of Gradient Type
- Authors: Benjamin Gess
- Preprint year: 2011
- First public date: 2011-04-21
- arXiv: 1104.4243
- Status: Published
- Publication type: Journal article
- Publication year: 2012
- Journal: Journal of functional analysis, 263 (2012) 8, pp. 2355-2383
- DOI: 10.1016/j.jfa.2012.07.001
Abstract
Unique existence of analytically strong solutions to stochastic partial differential equations (SPDE) with drift given by the subdifferential of a quasi-convex function and with general multiplicative noise is proven. The proof applies a genuinely new method of weighted Galerkin approximations based on the "distance" defined by the quasi-convex function. Spatial regularization of the initial condition analogous to the deterministic case is obtained. The results yield a unified framework which is applied to stochastic generalized porous media equations, stochastic generalized reaction diffusion equations and stochastic generalized degenerated p-Laplace equations. In particular, higher regularity for solutions of such SPDE is obtained.