The strong minimum principle for quasisuperminimizers of non-standard growth

Harjulehto, P.; Hästö, P.; Latvala, V.; Toivanen, O.

Annales de l'I.H.P. Analyse non linéaire, Tome 28 (2011) no. 5, pp. 731-742.

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.

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.

Classification : 49N60, 35B50, 35J60
Mots clés : Non-standard growth, Variable exponent, Dirichlet energy, Maximum principle, Minimum principle, Weak Harnack inequality, De Giorgi method

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