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

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.

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.

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

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