On the existence of bounded solutions for a nonlinear elliptic system

Mostrar todas las versiones(2)

This work deals with the system (−Δ)mu = a(x) vp, (−Δ)mv = b(x) uq with Dirichlet boundary condition in a domain Ω⊂Rn , where Ω is a ball if n ≥ 3 or a smooth perturbation of a ball when n = 2. We prove that, under appropriate conditions on the parameters (a, b, p, q, m, n), any nonnegative solution...

Descripción completa

Guardado en:
Detalles Bibliográficos
Autores principales: Durán, Ricardo Guillermo, Sanmartino, Marcela, Toschi, Marisa
Formato: Articulo Preprint
Lenguaje:Inglés
Publicado: 2011
Materias:
Matemática
Elliptic systems
A priori estimates
Critical exponents
Weighted sobolev spaces
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/98318
https://ri.conicet.gov.ar/11336/14930
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-98318
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Matemática
Elliptic systems
A priori estimates
Critical exponents
Weighted sobolev spaces
spellingShingle Matemática
Elliptic systems
A priori estimates
Critical exponents
Weighted sobolev spaces
Durán, Ricardo Guillermo
Sanmartino, Marcela
Toschi, Marisa
On the existence of bounded solutions for a nonlinear elliptic system
topic_facet Matemática
Elliptic systems
A priori estimates
Critical exponents
Weighted sobolev spaces
description This work deals with the system (−Δ)mu = a(x) vp, (−Δ)mv = b(x) uq with Dirichlet boundary condition in a domain Ω⊂Rn , where Ω is a ball if n ≥ 3 or a smooth perturbation of a ball when n = 2. We prove that, under appropriate conditions on the parameters (a, b, p, q, m, n), any nonnegative solution (u, v) of the system is bounded by a constant independent of (u, v). Moreover, we prove that the conditions are sharp in the sense that, up to some border case, the relation on the parameters are also necessary. The case m = 1 was considered by Souplet (Nonlinear Partial Differ Equ Appl 20:464–479, 2004). Our paper generalize to m ≥ 1 the results of that paper.
format Articulo
Preprint
author Durán, Ricardo Guillermo
Sanmartino, Marcela
Toschi, Marisa
author_facet Durán, Ricardo Guillermo
Sanmartino, Marcela
Toschi, Marisa
author_sort Durán, Ricardo Guillermo
title On the existence of bounded solutions for a nonlinear elliptic system
title_short On the existence of bounded solutions for a nonlinear elliptic system
title_full On the existence of bounded solutions for a nonlinear elliptic system
title_fullStr On the existence of bounded solutions for a nonlinear elliptic system
title_full_unstemmed On the existence of bounded solutions for a nonlinear elliptic system
title_sort on the existence of bounded solutions for a nonlinear elliptic system
publishDate 2011
url http://sedici.unlp.edu.ar/handle/10915/98318
https://ri.conicet.gov.ar/11336/14930
work_keys_str_mv AT duranricardoguillermo ontheexistenceofboundedsolutionsforanonlinearellipticsystem
AT sanmartinomarcela ontheexistenceofboundedsolutionsforanonlinearellipticsystem
AT toschimarisa ontheexistenceofboundedsolutionsforanonlinearellipticsystem
bdutipo_str Repositorios
_version_ 1764820492972195840

Ejemplares similares