Local existence conditions for an equations involving the p(x) -Laplacian with critical exponent in RN

The purpose of this paper is to formulate sufficient existence conditions for a critical equation involving the p(x)-Laplacian of the form (0.1) below posed in RN. This equation is critical in the sense that the source term has the form K(x) | u| q ( x ) - 2u with an exponent q that can be equal to...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Saintier, N., Silva, A.
Formato:	JOUR
Materias:	Concentration compactness Critical exponents Sobolev embedding Variable exponents
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_10219722_v24_n2_p_Saintier
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	todo:paper_10219722_v24_n2_p_Saintier
record_format	dspace
spelling	todo:paper_10219722_v24_n2_p_Saintier2023-10-03T15:56:44Z Local existence conditions for an equations involving the p(x) -Laplacian with critical exponent in RN Saintier, N. Silva, A. Concentration compactness Critical exponents Sobolev embedding Variable exponents The purpose of this paper is to formulate sufficient existence conditions for a critical equation involving the p(x)-Laplacian of the form (0.1) below posed in RN. This equation is critical in the sense that the source term has the form K(x) \| u\| q ( x ) - 2u with an exponent q that can be equal to the critical exponent p∗ at some points of RN including at infinity. The sufficient existence condition we find are local in the sense that they depend only on the behaviour of the exponents p and q near these points. We stress that we do not assume any symmetry or periodicity of the coefficients of the equation and that K is not required to vanish in some sense at infinity like in most existing results. The proof of these local existence conditions is based on a notion of localized best Sobolev constant at infinity and a refined concentration-compactness at infinity. © 2017, Springer International Publishing. Fil:Silva, A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_10219722_v24_n2_p_Saintier
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Concentration compactness Critical exponents Sobolev embedding Variable exponents
spellingShingle	Concentration compactness Critical exponents Sobolev embedding Variable exponents Saintier, N. Silva, A. Local existence conditions for an equations involving the p(x) -Laplacian with critical exponent in RN
topic_facet	Concentration compactness Critical exponents Sobolev embedding Variable exponents
description	The purpose of this paper is to formulate sufficient existence conditions for a critical equation involving the p(x)-Laplacian of the form (0.1) below posed in RN. This equation is critical in the sense that the source term has the form K(x) \| u\| q ( x ) - 2u with an exponent q that can be equal to the critical exponent p∗ at some points of RN including at infinity. The sufficient existence condition we find are local in the sense that they depend only on the behaviour of the exponents p and q near these points. We stress that we do not assume any symmetry or periodicity of the coefficients of the equation and that K is not required to vanish in some sense at infinity like in most existing results. The proof of these local existence conditions is based on a notion of localized best Sobolev constant at infinity and a refined concentration-compactness at infinity. © 2017, Springer International Publishing.
format	JOUR
author	Saintier, N. Silva, A.
author_facet	Saintier, N. Silva, A.
author_sort	Saintier, N.
title	Local existence conditions for an equations involving the p(x) -Laplacian with critical exponent in RN
title_short	Local existence conditions for an equations involving the p(x) -Laplacian with critical exponent in RN
title_full	Local existence conditions for an equations involving the p(x) -Laplacian with critical exponent in RN
title_fullStr	Local existence conditions for an equations involving the p(x) -Laplacian with critical exponent in RN
title_full_unstemmed	Local existence conditions for an equations involving the p(x) -Laplacian with critical exponent in RN
title_sort	local existence conditions for an equations involving the p(x) -laplacian with critical exponent in rn
url	http://hdl.handle.net/20.500.12110/paper_10219722_v24_n2_p_Saintier
work_keys_str_mv	AT saintiern localexistenceconditionsforanequationsinvolvingthepxlaplacianwithcriticalexponentinrn AT silvaa localexistenceconditionsforanequationsinvolvingthepxlaplacianwithcriticalexponentinrn
_version_	1782028011729584128

Local existence conditions for an equations involving the p(x) -Laplacian with critical exponent in RN

Ejemplares similares