-Harmonic functions with unbounded exponent in a subdomain
J.J. Manfredi
Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USAJ.D. Rossi
IMDEA Matemáticas, C-IX, Campus UAM, Madrid, SpainJ.M. Urbano
CMUC, Department of Mathematics, University of Coimbra, 3001-454 Coimbra, Portugal
Abstract
We study the Dirichlet problem in Ω, with on ∂Ω and in D, a subdomain of the reference domain Ω. The main issue is to give a proper sense to what a solution is. To this end, we consider the limit as of the solutions to the corresponding problem when , in particular, with in D. Under suitable assumptions on the data, we find that such a limit exists and that it can be characterized as the unique solution of a variational minimization problem which is, in addition, ∞-harmonic within D. Moreover, we examine this limit in the viscosity sense and find the boundary value problem it satisfies in the whole of Ω.
Cite this article
J.J. Manfredi, J.D. Rossi, J.M. Urbano, -Harmonic functions with unbounded exponent in a subdomain. Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), no. 6, pp. 2581–2595
DOI 10.1016/J.ANIHPC.2009.09.008