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Title: p(x)-Harmonic functions with unbounded exponent in a subdomain
Authors: Manfredi, Juan J. 
Rossi, Julio D. 
Urbano, José Miguel 
Keywords: p(x)-Laplacian; Infinity-Laplacian; Viscosity solutions
Issue Date: 2008
Publisher: Centro de Matemática da Universidade de Coimbra
Citation: Pré-Publicações DMUC. 08-46 (2008)
Abstract: We study the Dirichlet problem −div(|∇u|p(x)−2∇u) = 0 in , with u = f on @ and p(x) = ∞ in D, a subdomain of the reference domain . 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 p = 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. Moreover, we examine this limit in the viscosity sense and find an equation it satisfies.
Rights: openAccess
Appears in Collections:FCTUC Matemática - Vários

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