Page 1

Displaying 1 – 8 of 8

Showing per page

Γ -convergence of discrete approximations to interfaces with prescribed mean curvature

Giovanni Bellettini, Maurizio Paolini, Claudio Verdi (1990)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

The numerical approximation of the minimum problem: min A Ω F ~ A , is considered, where F ~ A = P Ω A + cos θ H n - 1 A Ω - A κ . The solution to this problem is a set A Ω R n with prescribed mean curvature κ and contact angle θ at the intersection of A with Ω . The functional F ~ is first relaxed with a sequence of nonconvex functionals defined in H 1 Ω which, in turn, are discretized by finite elements. The Γ -convergence of the discrete functionals to F ~ as well as the compactness of any sequence of discrete absolute minimizers are proven.

Γ-limits of convolution functionals

Luca Lussardi, Annibale Magni (2013)

ESAIM: Control, Optimisation and Calculus of Variations

We compute the Γ-limit of a sequence of non-local integral functionals depending on a regularization of the gradient term by means of a convolution kernel. In particular, as Γ-limit, we obtain free discontinuity functionals with linear growth and with anisotropic surface energy density.

Currently displaying 1 – 8 of 8

Page 1