In this paper we study the relaxation with respect to the $L^1$- norm of integral functionals of the calculus of variations, where the maps take values in the unit sphere. Here the volume term is supposed to be quasiconvex and with linear growth. In analogy with the unconstrained case, we show that the relaxed functional has an integral representation on BV, the space of functions of bounded variations.
Relaxation in BV of integral functionals defined on Sobolev functions with values in the unit sphere / Alicandro, R.; CORBO ESPOSITO, A.; Leone, Chiara. - In: JOURNAL OF CONVEX ANALYSIS. - ISSN 0944-6532. - STAMPA. - 14:(2007), pp. 69-98.
Relaxation in BV of integral functionals defined on Sobolev functions with values in the unit sphere
R. ALICANDRO;LEONE, CHIARA
2007
Abstract
In this paper we study the relaxation with respect to the $L^1$- norm of integral functionals of the calculus of variations, where the maps take values in the unit sphere. Here the volume term is supposed to be quasiconvex and with linear growth. In analogy with the unconstrained case, we show that the relaxed functional has an integral representation on BV, the space of functions of bounded variations.| File | Dimensione | Formato | |
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