Large solutions for the infinity Laplacian

Large solutions for the infinity Laplacian

In this paper, we study existence, uniqueness and asymptotic behavior near the boundary of solutions to in Ω with an explosive boundary condition u(x) → +∞ as x → ∂Ω. We find that there exists a solution if and only if q > 1. Moreover, when the domain Ω is sufficiently regular, such a solution is...

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Veröffentlicht in:Advances in calculus of variations 2008-10, Vol.1 (3), p.271-289
Hauptverfasser: Juutinen, Petri, Rossi, Julio D.
Format: Artikel
Sprache:eng
Schlagworte:
infinity Laplacian
Large solutions
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Beschreibung
Zusammenfassung:In this paper, we study existence, uniqueness and asymptotic behavior near the boundary of solutions to in Ω with an explosive boundary condition u(x) → +∞ as x → ∂Ω. We find that there exists a solution if and only if q > 1. Moreover, when the domain Ω is sufficiently regular, such a solution is unique and verifies as dist(x, ∂Ω) → 0.
ISSN:1864-8258
1864-8266
DOI:10.1515/ACV.2008.011