Large solutions for the infinity Laplacian

In this paper, we study existence, uniqueness and asymptotic behavior near the boundary of solutions to Δ∞u = (D2u(x) Du(x)/|Du(x)|).Du(x)/|Du(x)| = uq in Ω with an explosive boundary condition u(x) → + ∞ as x →∂Ω. We find that there exists a solution if and only if q > 1. Moreover, when the...

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Detalles Bibliográficos
Autor principal: Rossi, Julio Daniel
Publicado: 2008
Materias:
Infinity Laplacian
Large solutions
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_18648258_v1_n3_p271_Juutinen
http://hdl.handle.net/20.500.12110/paper_18648258_v1_n3_p271_Juutinen
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_18648258_v1_n3_p271_Juutinen
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spelling paper:paper_18648258_v1_n3_p271_Juutinen2023-06-08T16:29:37Z Large solutions for the infinity Laplacian Rossi, Julio Daniel Infinity Laplacian Large solutions In this paper, we study existence, uniqueness and asymptotic behavior near the boundary of solutions to Δ∞u = (D2u(x) Du(x)/|Du(x)|).Du(x)/|Du(x)| = uq in Ω with an explosive boundary condition u(x) → + ∞ as x →∂Ω. We find that there exists a solution if and only if q > 1. Moreover, when the domain Ω is sufficiently regular, such a solution is unique and verifies u(x) ∼(2(q + 1)/(q - 1)2)1/q-1 dist(x, ∂Ω) -2/q-1 © de Gruyter 2008. 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_18648258_v1_n3_p271_Juutinen http://hdl.handle.net/20.500.12110/paper_18648258_v1_n3_p271_Juutinen
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Infinity Laplacian
Large solutions
spellingShingle Infinity Laplacian
Large solutions
Rossi, Julio Daniel
Large solutions for the infinity Laplacian
topic_facet Infinity Laplacian
Large solutions
description In this paper, we study existence, uniqueness and asymptotic behavior near the boundary of solutions to Δ∞u = (D2u(x) Du(x)/|Du(x)|).Du(x)/|Du(x)| = uq in Ω with an explosive boundary condition u(x) → + ∞ as x →∂Ω. We find that there exists a solution if and only if q > 1. Moreover, when the domain Ω is sufficiently regular, such a solution is unique and verifies u(x) ∼(2(q + 1)/(q - 1)2)1/q-1 dist(x, ∂Ω) -2/q-1 © de Gruyter 2008.
author Rossi, Julio Daniel
author_facet Rossi, Julio Daniel
author_sort Rossi, Julio Daniel
title Large solutions for the infinity Laplacian
title_short Large solutions for the infinity Laplacian
title_full Large solutions for the infinity Laplacian
title_fullStr Large solutions for the infinity Laplacian
title_full_unstemmed Large solutions for the infinity Laplacian
title_sort large solutions for the infinity laplacian
publishDate 2008
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_18648258_v1_n3_p271_Juutinen
http://hdl.handle.net/20.500.12110/paper_18648258_v1_n3_p271_Juutinen
work_keys_str_mv AT rossijuliodaniel largesolutionsfortheinfinitylaplacian
_version_ 1768544750760099840

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