Minimizers of the variable exponent, non-uniformly convex Dirichlet energy

Petteri Harjulehto, Peter Hästö, Visa Latvala

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"We study energy minimizing properties of the function u = lim(lambda j) --> 1+ u(lambda j), where u(lambda j) is the solution to the p(lambda j) (.)-Laplacian Dirichlet problem with prescribed boundary values. Here p: Omega --> [1, infinity) is a variable exponent and p(lambda j) (x) = max{p(x),lambda(j)} for lambda(j) > 1. This problem leads in a natural way to a mixture of Sobolev and total variation norms. The main results are obtained under the assumption that p is strongly log-Holder continuous and bounded. To motivate our approach we also consider the one-dimensional case and give examples which justify our assumptions, The results can be applied in the analysis of a model for image restoration combining total variation and isotropic smoothing. (C) 2007 Elsevier Masson SAS. All rights reserved."
Original languageEnglish
JournalJournal de Mathematiques Pures et Appliquées
Issue number2
Pages (from-to)174-197
Number of pages24
Publication statusPublished - 2008
MoE publication typeA1 Journal article-refereed

Fields of Science

  • 111 Mathematics

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