L energies on discontinuous functions

Roberto Alicandro, Andrea Braides, Marco Cicalese

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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.

Original languageEnglish
Pages (from-to)905-928
Number of pages24
JournalDiscrete and Continuous Dynamical Systems- Series A
Issue number5
StatePublished - May 2005
Externally publishedYes


  • Functions of bounded variation
  • L energies
  • Lower semicontinuity


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