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.
On the Gamma Convergence of Functionals Defined Over Pairs of Measures and Energy-Measures
Caroccia M.;
2020-01-01
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.| File | Dimensione | Formato | |
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