Strong solutions for stochastic partial differential equations of gradient type
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Publication:1760161
DOI10.1016/J.JFA.2012.07.001zbMATH Open1267.60072arXiv1104.4243OpenAlexW2964124635MaRDI QIDQ1760161
Author name not available (Why is that?)
Publication date: 13 November 2012
Published in: (Search for Journal in Brave)
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.
Full work available at URL: https://arxiv.org/abs/1104.4243
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