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Article Dans Une Revue Annali della Scuola Normale Superiore di Pisa, Classe di Scienze Année : 2007

Sobolev versus Hölder local minimizers and existence of multiple solutions for a singular quasilinear equation

Résumé

In a bounded domain with smooth boundary, the authors pose the problem of finding a function that is strictly positive inside the domain, vanishing on the boundary of the domain and satisfies a quasilinear differential equation, inside the domain, whose left-hand side has the $p$-Laplace operator of the unknown function and whose right-hand side is a linear combination of the unknown function in positive and negative powers. The main result of the paper, which is a proof of the existence of at least two weak solutions of the above-mentioned problem in the corresponding Sobolev spaces, is obtained by a development of the well-known variational method. In addition, the authors prove that the weak solutions belong to Hölder spaces. They also establish a strong comparison principle.
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Dates et versions

hal-00982426 , version 1 (23-04-2014)

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  • HAL Id : hal-00982426 , version 1

Citer

Jacques Giacomoni, Ian Schindler, Peter Takáč. Sobolev versus Hölder local minimizers and existence of multiple solutions for a singular quasilinear equation. Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 2007, 1, pp.117-158. ⟨hal-00982426⟩
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