p (x)-Harmonic functions with unbounded exponent in a subdomain

J. J. Manfredi, J. D. Rossi, J. M. Urbano

Research output: Contribution to journalArticlepeer-review

28 Scopus citations


We study the Dirichlet problem - div (| ∇ u |p (x) - 2 ∇ u) = 0 in Ω, with u = f on ∂Ω and p (x) = ∞ 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 n → ∞ of the solutions un to the corresponding problem when pn (x) = p (x) ∧ n, in particular, with pn = n 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. © 2009 Elsevier Masson SAS. All rights reserved.
Original languageEnglish (US)
Pages (from-to)2581-2595
Number of pages15
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Issue number6
StatePublished - Jan 1 2009
Externally publishedYes

Bibliographical note

Generated from Scopus record by KAUST IRTS on 2023-02-15

ASJC Scopus subject areas

  • Mathematical Physics
  • Analysis


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