Estudo GeralThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.https://estudogeral.sib.uc.pt2019-08-21T14:04:19Z2019-08-21T14:04:19Z5021Limits as p(x) of p(x)-harmonic functionsManfredi, Juan J.Rossi, Julio D.Urbano, José Miguelhttp://hdl.handle.net/10316/111752019-06-01T21:20:15Z2009-01-01T00:00:00ZTitle: Limits as p(x) of p(x)-harmonic functions Authors: Manfredi, Juan J.; Rossi, Julio D.; Urbano, José Miguel Abstract: In this note we study the limit as p(x) ! 1of solutions to − p(x)u = 0 in a domain , with Dirichlet boundary conditions. Our approach consists in considering sequences of variable exponents converging uniformly to +1 and analyzing how the corresponding solutions of the problem converge and what equation is satisfied by the limit. 2009-01-01T00:00:00Zp(x)-Harmonic functions with unbounded exponent in a subdomainManfredi, Juan J.Rossi, Julio D.Urbano, José Miguelhttp://hdl.handle.net/10316/112222019-06-01T21:20:19Z2008-01-01T00:00:00ZTitle: p(x)-Harmonic functions with unbounded exponent in a subdomain Authors: Manfredi, Juan J.; Rossi, Julio D.; Urbano, José Miguel 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. 2008-01-01T00:00:00Z