Large solutions to the p-Laplacian for large p

In this work we consider the behaviour for large values of p of the unique positive weak solution u p to Δ p u = u q in Ω, u = +∞ on partial Ω, where q > p - 1. We take q = q(p) and analyze the limit of u p as p → ∞. We find that when q(p)/p → Q the behaviour strongly depends on Q. If 1 &...

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Autor principal: Rossi, Julio Daniel
Publicado: 2008
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09442669_v31_n2_p187_GarciaMelian
http://hdl.handle.net/20.500.12110/paper_09442669_v31_n2_p187_GarciaMelian
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_09442669_v31_n2_p187_GarciaMelian
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spelling paper:paper_09442669_v31_n2_p187_GarciaMelian2023-06-08T15:53:45Z Large solutions to the p-Laplacian for large p Rossi, Julio Daniel In this work we consider the behaviour for large values of p of the unique positive weak solution u p to Δ p u = u q in Ω, u = +∞ on partial Ω, where q > p - 1. We take q = q(p) and analyze the limit of u p as p → ∞. We find that when q(p)/p → Q the behaviour strongly depends on Q. If 1 < Q < ∞ then solutions converge uniformly in compacts to a viscosity solution of max{-Δ{u}, -|∇ u| +uQ \\} = 0 with u = +∞ on Ω. If Q = 1 then solutions go to ∞ in the whole Ω and when Q = ∞ solutions converge to 1 uniformly in compact subsets of Ω, hence the boundary blow-up is lost in the limit. © 2007 Springer-Verlag. Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2008 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09442669_v31_n2_p187_GarciaMelian http://hdl.handle.net/20.500.12110/paper_09442669_v31_n2_p187_GarciaMelian
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description In this work we consider the behaviour for large values of p of the unique positive weak solution u p to Δ p u = u q in Ω, u = +∞ on partial Ω, where q > p - 1. We take q = q(p) and analyze the limit of u p as p → ∞. We find that when q(p)/p → Q the behaviour strongly depends on Q. If 1 < Q < ∞ then solutions converge uniformly in compacts to a viscosity solution of max{-Δ{u}, -|∇ u| +uQ \\} = 0 with u = +∞ on Ω. If Q = 1 then solutions go to ∞ in the whole Ω and when Q = ∞ solutions converge to 1 uniformly in compact subsets of Ω, hence the boundary blow-up is lost in the limit. © 2007 Springer-Verlag.
author Rossi, Julio Daniel
spellingShingle Rossi, Julio Daniel
Large solutions to the p-Laplacian for large p
author_facet Rossi, Julio Daniel
author_sort Rossi, Julio Daniel
title Large solutions to the p-Laplacian for large p
title_short Large solutions to the p-Laplacian for large p
title_full Large solutions to the p-Laplacian for large p
title_fullStr Large solutions to the p-Laplacian for large p
title_full_unstemmed Large solutions to the p-Laplacian for large p
title_sort large solutions to the p-laplacian for large p
publishDate 2008
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09442669_v31_n2_p187_GarciaMelian
http://hdl.handle.net/20.500.12110/paper_09442669_v31_n2_p187_GarciaMelian
work_keys_str_mv AT rossijuliodaniel largesolutionstotheplaplacianforlargep
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