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Article type: Research Article
Authors: Fernández Bonder, Juliána; b; * | Saintier, Nicolasc; d | Silva, Analíaa; b
Affiliations: [a] IMAS, CONICET, Universidad de Buenos Aires, Buenos Aires, Argentina | [b] Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Buenos Aires, Argentina. E-mails: [email protected], [email protected] | [c] Instituto de Ciencias, Universidad Nacional de General Sarmiento, Buenos Aires, Argentina | [d] Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Buenos Aires, Argentina. E-mails: [email protected], [email protected]
Correspondence: [*] Corresponding author: Julián Fernández Bonder, IMAS, CONICET and Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I (1428), Buenos Aires, Argentina. E-mail: [email protected]; URL: http://mate.dm.uba.ar/~jfbonder.
Abstract: In this paper we study sufficient local conditions for the existence of non-trivial solution to a critical equation for the p(x)-Laplacian where the critical term is placed as a source through the boundary of the domain. The proof relies on a suitable generalization of the concentration–compactness principle for the trace embedding for variable exponent Sobolev spaces and the classical mountain pass theorem.
Keywords: Sobolev embedding, variable exponents, critical exponents, concentration compactness
DOI: 10.3233/ASY-151289
Journal: Asymptotic Analysis, vol. 93, no. 1-2, pp. 161-185, 2015
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