ESAIM: Control, Optimisation and Calculus of Variations (ESAIM: COCV)

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ESAIM: COCV
DOI: 10.1051/cocv:2008026

Relaxation of isotropic functionals with linear growth defined on manifold constrained Sobolev mappings

Domenico Mucci

Dipartimento di Matematica dell'Università di Parma, Viale G. P. Usberti 53/A, 43100 Parma, Italy; domenico.mucci@unipr.it

(Received April 19, 2007. Published online March 28, 2008.)

Abstract
In this paper we study the lower semicontinuous envelope with respect to the L¹-topology of a class of isotropic functionals with linear growth defined on mappings from the n-dimensional ball into ${\mathbb R}^{N}$ that are constrained to take values into a smooth submanifold ${\cal Y}$ of ${\mathbb R}^{N}$ .

Mathematics Subject Classification. 49J45, 49Q20

Key words: Relaxation, manifold constrain, BV functions

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