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...

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Autor principal: Silva, Analia Concepcion
Publicado: 2017
Materias:
Concentration compactness
Critical exponents
Sobolev embedding
Variable exponents
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10219722_v24_n2_p_Saintier
http://hdl.handle.net/20.500.12110/paper_10219722_v24_n2_p_Saintier
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling paper:paper_10219722_v24_n2_p_Saintier2023-06-08T16:00:05Z Local existence conditions for an equations involving the p(x) -Laplacian with critical exponent in RN Silva, Analia Concepcion 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. 2017 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10219722_v24_n2_p_Saintier 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
Silva, Analia Concepcion
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.
author Silva, Analia Concepcion
author_facet Silva, Analia Concepcion
author_sort Silva, Analia Concepcion
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
publishDate 2017
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10219722_v24_n2_p_Saintier
http://hdl.handle.net/20.500.12110/paper_10219722_v24_n2_p_Saintier
work_keys_str_mv AT silvaanaliaconcepcion localexistenceconditionsforanequationsinvolvingthepxlaplacianwithcriticalexponentinrn
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