We consider a strongly nonlinear monotone elliptic problem in generalized Orlicz-Musielak spaces. We assume neither a Δ2 nor ∇2-condition for an inhomogeneous and anisotropic N-function but assume it to be log-Hölder continuous with respect to x. We show the existence of weak solutions to the zero Dirichlet boundary value problem. Within the proof the L ∞-truncation method is coupled with a special version of the Minty-Browder trick for non-reflexive and non-separable Banach spaces.
@article{bwmeta1.element.doi-10_2478_s11533-012-0126-3,
author = {Piotr Gwiazda and Piotr Minakowski and Aneta Wr\'oblewska-Kami\'nska},
title = {Elliptic problems in generalized Orlicz-Musielak spaces},
journal = {Open Mathematics},
volume = {10},
year = {2012},
pages = {2019-2032},
zbl = {1268.35056},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0126-3}
}
Piotr Gwiazda; Piotr Minakowski; Aneta Wróblewska-Kamińska. Elliptic problems in generalized Orlicz-Musielak spaces. Open Mathematics, Tome 10 (2012) pp. 2019-2032. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0126-3/
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