JournalsrsmupVol. 130pp. 155–168

On the Jump set of Solutions of the Total Variation Flow

  • Vicent Caselles

    Universitat Pompeu-Fabra, Barcelona, Spain
  • Khalid Jalalzai

    Ecole Polytechnique, Palaiseau, France
  • Matteo Novaga

    Università di Pisa, Italy
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Abstract

We show that the jump set of the solution of the minimizing Total Variation flow decreases with time for any initial condition in BV(Ω)LN(Ω)BV({\Omega} )\cap L^N({\Omega} ). We prove that the size of the jump also decreases with time.

Cite this article

Vicent Caselles, Khalid Jalalzai, Matteo Novaga, On the Jump set of Solutions of the Total Variation Flow. Rend. Sem. Mat. Univ. Padova 130 (2013), pp. 155–168

DOI 10.4171/RSMUP/130-5