Elliptic problems in generalized Orlicz-Musielak spaces

Piotr Gwiazda; Piotr Minakowski; Aneta Wróblewska-Kamińska

Open Mathematics (2012)

  • Volume: 10, Issue: 6, page 2019-2032
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Piotr Gwiazda, Piotr Minakowski, and Aneta Wróblewska-Kamińska. "Elliptic problems in generalized Orlicz-Musielak spaces." Open Mathematics 10.6 (2012): 2019-2032. <http://eudml.org/doc/269691>.

@article{PiotrGwiazda2012,
abstract = {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.},
author = {Piotr Gwiazda, Piotr Minakowski, Aneta Wróblewska-Kamińska},
journal = {Open Mathematics},
keywords = {Orlicz Spaces; Nonlinear elliptic equations; log-Hölder continuity; Modular topology; Orlicz spaces; nonlinear elliptic equations; modular topology},
language = {eng},
number = {6},
pages = {2019-2032},
title = {Elliptic problems in generalized Orlicz-Musielak spaces},
url = {http://eudml.org/doc/269691},
volume = {10},
year = {2012},
}

TY - JOUR
AU - Piotr Gwiazda
AU - Piotr Minakowski
AU - Aneta Wróblewska-Kamińska
TI - Elliptic problems in generalized Orlicz-Musielak spaces
JO - Open Mathematics
PY - 2012
VL - 10
IS - 6
SP - 2019
EP - 2032
AB - 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.
LA - eng
KW - Orlicz Spaces; Nonlinear elliptic equations; log-Hölder continuity; Modular topology; Orlicz spaces; nonlinear elliptic equations; modular topology
UR - http://eudml.org/doc/269691
ER -

References

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