A variational problem for multifunctions with interaction between leaves
JournalArticle (Originalarbeit in einer wissenschaftlichen Zeitschrift)
ID 2189528
Author(s) Acerbi, Emilio; Crippa, Gianluca; Mucci, Domenico
Author(s) at UniBasel Crippa, Gianluca
Year 2012
Title A variational problem for multifunctions with interaction between leaves
Journal ESAIM: Control, Optimisation and Calculus of Variations
Volume 18
Number 4
Pages / Article-Number 1178-1206
Abstract We discuss a variational problem defined on couples of functions that are constrained to take values into the 2-dimensional unit sphere. The energy functional contains, besides standard Dirichlet energies, a non-local interaction term that depends on the distance between the gradients of the two functions. Different gradients are preferred or penalized in this model, in dependence of the sign of the interaction term. In this paper we study the lower semicontinuity and the coercivity of the energy and we find an explicit representation formula for the relaxed energy. Moreover, we discuss the behavior of the energy in the case when we consider multifunctions with two leaves rather than couples of functions.
Publisher EDP Sciences
ISSN/ISBN 1292-8119 ; 1262-3377
edoc-URL http://edoc.unibas.ch/49502/
Full Text on edoc Available
Digital Object Identifier DOI 10.1051/cocv/2011195
ISI-Number WOS:000313504300014
Document type (ISI) Article

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