Strong solutions for stochastic partial differential equations of gradient type

Gess B (2012)
Journal of Functional Analysis 263(8): 2355-2383.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
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. (C) 2012 Elsevier Inc. All rights reserved.
Stichworte
Stochastic; Stochastic porous medium equation; Subdifferential; Regularity; Stochastic partial differential equations; Strong solutions; Stochastic p-Laplace equation; reaction-diffusion equation
Erscheinungsjahr
2012
Zeitschriftentitel
Journal of Functional Analysis
Band
263
Ausgabe
8
Seite(n)
2355-2383
ISSN
0022-1236
Page URI
https://pub.uni-bielefeld.de/record/2536060

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Gess B. Strong solutions for stochastic partial differential equations of gradient type. Journal of Functional Analysis. 2012;263(8):2355-2383.
Gess, B. (2012). Strong solutions for stochastic partial differential equations of gradient type. Journal of Functional Analysis, 263(8), 2355-2383. doi:10.1016/j.jfa.2012.07.001
Gess, B. (2012). Strong solutions for stochastic partial differential equations of gradient type. Journal of Functional Analysis 263, 2355-2383.
Gess, B., 2012. Strong solutions for stochastic partial differential equations of gradient type. Journal of Functional Analysis, 263(8), p 2355-2383.
B. Gess, “Strong solutions for stochastic partial differential equations of gradient type”, Journal of Functional Analysis, vol. 263, 2012, pp. 2355-2383.
Gess, B.: Strong solutions for stochastic partial differential equations of gradient type. Journal of Functional Analysis. 263, 2355-2383 (2012).
Gess, Benjamin. “Strong solutions for stochastic partial differential equations of gradient type”. Journal of Functional Analysis 263.8 (2012): 2355-2383.