We study necessary and sufficient conditions for the lower-semicontinuity of one-dimensional energies defined on (BV and) SBV of the model form F(u) = sup f (u′) V sup g ([u]), and prove a relaxation theorem. We apply these results to the study of problems with Dirichlet boundary conditions, highlighting a complex behaviour of solutions. We draw a comparison with the parallel theory for integral energies on SBV.
L∞ energies on discontinuous functions / Alicandro, R.; Braides, A.; Cicalese, M.. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES B.. - ISSN 1531-3492. - 12:5(2005), pp. 905-928.
L∞ energies on discontinuous functions
Alicandro, R.;Braides, A.
;Cicalese, M.
2005-01-01
Abstract
We study necessary and sufficient conditions for the lower-semicontinuity of one-dimensional energies defined on (BV and) SBV of the model form F(u) = sup f (u′) V sup g ([u]), and prove a relaxation theorem. We apply these results to the study of problems with Dirichlet boundary conditions, highlighting a complex behaviour of solutions. We draw a comparison with the parallel theory for integral energies on SBV.File in questo prodotto:
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