Calculus of Variations and Geometric Measure Theory
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M. Caroccia - R. Cristoferi

On the Gamma convergence of functionals defined over pairs of measures and energy-measures

created by cristoferi on 06 Sep 2019
modified on 25 Sep 2019

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Submitted Paper

Inserted: 6 sep 2019
Last Updated: 25 sep 2019

Year: 2019

Abstract:

A novel general framework for the study of $\Gamma$-convergence of functionals defined over pairs of measures and energy-measures is introduced. This theory allows us to identify the $\Gamma$-limit of these kind of functionals by knowing the $ \Gamma$-limit of the underlying energies. In particular, the interaction between the functionals and the underlying energies results, in the case these latter converge to a non continuous energy, in an additional effect in the relaxation process. This study was motivated by a question in the context of epitaxial growth evolution with adatoms. Interesting cases of application of the general theory are also presented.


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