On minimization of a non-convex functional in variable exponent spaces

Gerardo R. Chacón; Renato Colucci; Humberto Rafeiro; Andrés Vargas

doi:10.1142/S0129167X14500116

On minimization of a non-convex functional in variable exponent spaces

Gerardo R. Chacón, Renato Colucci, Humberto Rafeiro, Andrés Vargas

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

We study the existence of minimizers of a regularized non-convex functional in the context of variable exponent Sobolev spaces by application of the direct method in the calculus of variations. The results are new even in the framework of classical Lebesgue spaces.

Original language	English
Article number	1450011
Journal	International Journal of Mathematics
Volume	25
Issue number	1
DOIs	https://doi.org/10.1142/S0129167X14500116
Publication status	Published - Jan 2014
Externally published	Yes

Keywords

Direct method
Variable Lebesgue spaces
Variable Sobolev spaces
Variable exponent functional

ASJC Scopus subject areas

Mathematics(all)

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10.1142/S0129167X14500116

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title = "On minimization of a non-convex functional in variable exponent spaces",

abstract = "We study the existence of minimizers of a regularized non-convex functional in the context of variable exponent Sobolev spaces by application of the direct method in the calculus of variations. The results are new even in the framework of classical Lebesgue spaces.",

keywords = "Direct method, Variable Lebesgue spaces, Variable Sobolev spaces, Variable exponent functional",

author = "Chac{\'o}n, {Gerardo R.} and Renato Colucci and Humberto Rafeiro and Andr{\'e}s Vargas",

note = "Funding Information: The authors would like to thank the anonymous referee for useful remarks that helped to improve the presentation. This paper was financially supported under the project id-pry: 004605 of Faculty of Sciences of Pontificia Universidad Javeriana, Bogot{\'a} D.C., Colombia.",

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AU - Colucci, Renato

AU - Rafeiro, Humberto

AU - Vargas, Andrés

N1 - Funding Information: The authors would like to thank the anonymous referee for useful remarks that helped to improve the presentation. This paper was financially supported under the project id-pry: 004605 of Faculty of Sciences of Pontificia Universidad Javeriana, Bogotá D.C., Colombia.

PY - 2014/1

Y1 - 2014/1

N2 - We study the existence of minimizers of a regularized non-convex functional in the context of variable exponent Sobolev spaces by application of the direct method in the calculus of variations. The results are new even in the framework of classical Lebesgue spaces.

AB - We study the existence of minimizers of a regularized non-convex functional in the context of variable exponent Sobolev spaces by application of the direct method in the calculus of variations. The results are new even in the framework of classical Lebesgue spaces.

KW - Direct method

KW - Variable Lebesgue spaces

KW - Variable Sobolev spaces

KW - Variable exponent functional

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On minimization of a non-convex functional in variable exponent spaces

Abstract

Keywords

ASJC Scopus subject areas

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