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A variational problem for multifunctions with interaction between leaves

Acerbi, Emilio and Crippa, Gianluca and Mucci, Domenico. (2012) A variational problem for multifunctions with interaction between leaves. ESAIM: Control, Optimisation and Calculus of Variations, 18 (4). pp. 1178-1206.

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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.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Analysis (Crippa)
UniBasel Contributors:Crippa, Gianluca
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:EDP Sciences
ISSN:1292-8119
e-ISSN:1262-3377
Note:Publication type according to Uni Basel Research Database: Journal article
Language:English
Identification Number:
Last Modified:04 May 2017 07:47
Deposited On:04 May 2017 07:47

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