Remarks on some minimization problems associated with BV norms

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The purpose of this paper is twofold. Firstly I present an optimal regularity result for minimizers of a 1D convex functional involving the BV-norm, under Neumann boundary condition. This functional is a simplified version of models occuring in Image Processing. Secondly I investigate the existence of minimizers for the same functional under Dirichlet boundary condition. Surprisingly, this turns out to be a delicate issue, which is still widely open.

Original languageEnglish (US)
Pages (from-to)7013-7029
Number of pages17
JournalDiscrete and Continuous Dynamical Systems- Series A
Issue number12
StatePublished - 2019

All Science Journal Classification (ASJC) codes

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


  • Bounded variation
  • Dirichlet boundary condition
  • Neumann boundary condition
  • Regularity of minimizers


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