Anisotropic parabolic problems with slowly or rapidly growing terms

Agnieszka Świerczewska-Gwiazda. "Anisotropic parabolic problems with slowly or rapidly growing terms." Colloquium Mathematicae 134.1 (2014): 113-130. <http://eudml.org/doc/283565>.

@article{AgnieszkaŚwierczewska2014,
abstract = {We consider an abstract parabolic problem in a framework of maximal monotone graphs, possibly multi-valued, with growth conditions formulated with the help of an x-dependent N-function. The main novelty of the paper consists in the lack of any growth restrictions on the N-function combined with its anisotropic character, namely we allow the dependence on all the directions of the gradient, not only on its absolute value. This leads to using the notion of modular convergence and studying in detail the question of density of compactly supported smooth functions with respect to modular convergence.},
author = {Agnieszka Świerczewska-Gwiazda},
journal = {Colloquium Mathematicae},
keywords = {Musielak-Orlicz spaces; modular convergence; nonlinear parabolic inclusion; maximal monotone graph},
language = {eng},
number = {1},
pages = {113-130},
title = {Anisotropic parabolic problems with slowly or rapidly growing terms},
url = {http://eudml.org/doc/283565},
volume = {134},
year = {2014},
}

TY - JOUR
AU - Agnieszka Świerczewska-Gwiazda
TI - Anisotropic parabolic problems with slowly or rapidly growing terms
JO - Colloquium Mathematicae
PY - 2014
VL - 134
IS - 1
SP - 113
EP - 130
AB - We consider an abstract parabolic problem in a framework of maximal monotone graphs, possibly multi-valued, with growth conditions formulated with the help of an x-dependent N-function. The main novelty of the paper consists in the lack of any growth restrictions on the N-function combined with its anisotropic character, namely we allow the dependence on all the directions of the gradient, not only on its absolute value. This leads to using the notion of modular convergence and studying in detail the question of density of compactly supported smooth functions with respect to modular convergence.
LA - eng
KW - Musielak-Orlicz spaces; modular convergence; nonlinear parabolic inclusion; maximal monotone graph
UR - http://eudml.org/doc/283565
ER -