JournalsaihpcVol. 28, No. 5pp. 731–742

The strong minimum principle for quasisuperminimizers of non-standard growth

  • P. Harjulehto

    Department of Mathematics and Statistics, P.O. Box 68, FI-00014 University of Helsinki, Finland

  • P. Hästö

    Department of Mathematical Sciences, P.O. Box 3000, FI-90014 University of Oulu, Finland

  • V. Latvala

    Department of Physics and Mathematics, University of Eastern Finland, P.O. Box 111, FI-80101 Joensuu, Finland

  • O. Toivanen

    Department of Physics and Mathematics, University of Eastern Finland, P.O. Box 111, FI-80101 Joensuu, Finland
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Abstract

We prove the strong minimum principle for non-negative quasisuperminimizers of the variable exponent Dirichlet energy integral under the assumption that the exponent has modulus of continuity slightly more general than Lipschitz. The proof is based on a new version of the weak Harnack estimate.

Résumé

Nous prouvons le fort principe du minimum pour des quasisuperminimizeurs non-négatifs de problème de Dirichlet de lʼexposant variable en supposant que lʼexposant a le module de continuité un peu plus général que Lipschitz. La démonstration est fondée sur une nouvelle version de la faible inégalité de Harnack.

Cite this article

P. Harjulehto, P. Hästö, V. Latvala, O. Toivanen, The strong minimum principle for quasisuperminimizers of non-standard growth. Ann. Inst. H. Poincaré Anal. Non Linéaire 28 (2011), no. 5, pp. 731–742

DOI 10.1016/J.ANIHPC.2011.06.001