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Article Dans Une Revue Annali della Scuola Normale Superiore di Pisa, Classe di Scienze Année : 2017

Monotonicity in half-spaces of positive solutions to -Delta(p)u = f(u) in the case p > 2

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Résumé

We consider weak distributional solutions to the equation -Delta(p)u f(u) in half-spaces under zero Dirichlet boundary condition. We assume that the nonlinearity is positive and superlinear at zero. For p > 2 (the case 1 < p <= 2 is already known) we prove that any positive solution is strictly monotone increasing in the direction orthogonal to the boundary of the half-space. As a consequence we deduce some Liouville-type theorems for the Lane-Emden-equation. Furthermore any nonnegative solution turns out to be C-2,C- (alpha) smooth.
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Dates et versions

hal-03621419 , version 1 (28-03-2022)

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  • HAL Id : hal-03621419 , version 1

Citer

Alberto Farina, Luigi Montoro, Berardino Sciunzi. Monotonicity in half-spaces of positive solutions to -Delta(p)u = f(u) in the case p > 2. Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 2017, 17 (4), pp.1207-1229. ⟨hal-03621419⟩
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