hal-00709073, version 1
Boundary trace of positive solutions of supercritical semilinear elliptic equations in dihedral domains
Résumé : We study the generalized boundary value problem for (E)\; $-\Delta u+|u|^{q-1}u=0$ in a dihedral domain $\Gw$, when $q>1$ is supercritical. The value of the critical exponent can take only a finite number of values depending on the geometry of $\Gw$. When $\gm$ is a bounded Borel measure in a k-wedge, we give necessary and sufficient conditions in order it be the boundary value of a solution of (E). We also give conditions which ensure that a boundary compact subset is removable. These conditions are expressed in terms of Bessel capacities $B_{s,q'}$ in $\BBR^{N-k}$ where $s$ depends on the characteristics of the wedge. This allows us to describe the boundary trace of a positive solution of (E)
- 1 :
- Technion - Israel Institute of Technology
- 2 :
- Université François Rabelais - Tours – CNRS : UMR7350
- Domaine : Mathématiques/Equations aux dérivées partielles
- Mots-clés : Laplacian – Poisson potential – Borel measures – Besov spaces – harmonic lifting – Bessel capacities.
- hal-00709073, version 1
- http://hal.archives-ouvertes.fr/hal-00709073
- oai:hal.archives-ouvertes.fr:hal-00709073
- Contributeur :
- Soumis le : Dimanche 17 Juin 2012, 15:02:02
- Dernière modification le : Dimanche 17 Juin 2012, 15:49:02
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