On the Gamma Convergence of Functionals Defined Over Pairs of Measures and Energy-Measures

Marco Caroccia, Riccardo Cristoferi

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Abstract

A novel general framework for the study of Γ -convergence of functionals defined over pairs of measures and energy-measures is introduced. This theory allows us to identify the Γ -limit of these kind of functionals by knowing the Γ -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.

Original languageEnglish
Pages (from-to)1723-1769
Number of pages47
JournalJournal of Nonlinear Science
Volume30
Issue number4
Early online date19 Mar 2020
DOIs
Publication statusPublished - Aug 2020

Keywords

  • Convex sub-additive envelope
  • Functionals defined on measures
  • Gamma-convergence
  • Phase-field models

ASJC Scopus subject areas

  • Modelling and Simulation
  • Engineering(all)
  • Applied Mathematics

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