A variational problem for couples of functions and multifunctions with interaction between leaves
Emilio Acerbi, Gianluca Crippa, Domenico Mucci (2012)
ESAIM: Control, Optimisation and Calculus of Variations
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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...