On the approximation of SBV functions, by guido de philippis

Guido De Philippis, Nicola Fusco, Aldo Pratelli

Research output: Contribution to journalArticle

Abstract

In this paper we deal with the approximation of SBV functions in the strong BV topology. In particular, we provide three approximation results. The first one, Theorem A, concerns general SBV functions; the second one, Theorem B, concerns SBV functions with absolutely continuous part of the gradient in L p, p > 1; and the third one, Theorem C, concerns SBV p functions, that is, those SBV functions for which not only the absolutely continuous part of the gradient is in L p, but also the jump set has finite HN-1-measure. The last result generalizes the previously known approximation theorems for SBV p functions, see [5, 7]. As we discuss, the first and the third result are sharp. We conclude with a simple application of our results.

Original languageEnglish (US)
Pages (from-to)369-413
Number of pages45
JournalAtti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni
Volume28
Issue number2
DOIs
StatePublished - 2017

Keywords

  • Approximation
  • Free discontinuity problems
  • SBV functions

ASJC Scopus subject areas

  • Mathematics(all)

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