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

created by cristoferi on 06 Sep 2019
modified on 08 Oct 2020

[BibTeX]

Published Paper

Inserted: 6 sep 2019
Last Updated: 8 oct 2020

Journal: Journal of Nonlinear Science
Volume: 30
Number: 4
Pages: 1723-1769
Year: 2020
Doi: https://doi.org/10.1007/s00332-020-09623-y

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.