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 ([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..
Alicandro, R., Braides, A., Cicalese, M. (2005). L-infinity energies on discontinuous functions. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 12(5), 905-928.
L-infinity energies on discontinuous functions
BRAIDES, ANDREA;
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 ([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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