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Double Γ-Convergence and Application to Energy Functionals

Part of: Existence theories Manifolds

Published online by Cambridge University Press:  28 July 2014

Mao-Sheng Chang
Mao-Sheng Chang*
Affiliation:
Department of Mathematics, Fu Jen Catholic University, 510 Zhongzheng Road, Xinzhuang District, New Taipei City 24205, Taiwan, ([email protected])
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Abstract

We introduce a ‘double’ version of Γ-convergence, which we have named ‘double Γ-convergence’, and apply it to obtain the Γ-limit of double-perturbed energy functionals as p → 1 and p → +∞, respectively. The limit of (p, q)-type capacity as p → 1 and p → +∞, respectively, is also obtained in this manner.

Keywords

Gamma-convergencefunctions of bounded variationscapacity

MSC classification

Primary: 49J45: Methods involving semicontinuity and convergence; relaxation
Secondary: 49Q20: Variational problems in a geometric measure-theoretic setting
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 58 , Issue 1 , February 2015 , pp. 107 - 124
Copyright
Copyright © Edinburgh Mathematical Society 2015 

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