Please use this identifier to cite or link to this item: http://hdl.handle.net/10316/11222
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.
URI: http://hdl.handle.net/10316/11222
Rights: openAccess
Appears in Collections:FCTUC Matemática - Vários

Files in This Item:
File Description SizeFormat 
p(x)-Harmonic functions with unbounded exponent.pdf161.61 kBAdobe PDFView/Open
Show full item record

Page view(s) 50

268
checked on Jun 12, 2019

Download(s)

19
checked on Jun 12, 2019

Google ScholarTM

Check


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.