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

Petteri Harjulehto, Peter Hästö, Visa Latvala

Research output: Contribution to journalArticleScientificpeer-review

Abstract

"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
Volume89
Issue number2
Pages (from-to)174-197
Number of pages24
ISSN0021-7824
DOIs
Publication statusPublished - 2008
MoE publication typeA1 Journal article-refereed

Fields of Science

  • 111 Mathematics

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