Geodesic
Anisotropic parabolic problems with slowly or rapidly growing terms
Agnieszka Świerczewska-Gwiazda1
1 Institute of Applied Mathematics and Mechanics University of Warsaw 02-097 Warszawa, Poland
Colloquium Mathematicum, Tome 134 (2014) no. 1, pp. 113-130

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/cm134-1-5
Keywords: consider abstract parabolic problem framework maximal monotone graphs possibly multi valued growth conditions formulated help x dependent n function main novelty paper consists lack growth restrictions function combined its anisotropic character namely allow dependence directions gradient only its absolute value leads using notion modular convergence studying detail question density compactly supported smooth functions respect modular convergence

Agnieszka Świerczewska-Gwiazda 1

1 Institute of Applied Mathematics and Mechanics University of Warsaw 02-097 Warszawa, Poland 
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Agnieszka Świerczewska-Gwiazda. Anisotropic parabolic problems with slowly or rapidly growing terms. Colloquium Mathematicum, Tome 134 (2014) no. 1, pp. 113-130. doi: 10.4064/cm134-1-5

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