Rendiconti del Seminario Matematico della Università di Padova


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Volume 130, 2013, pp. 155–168
DOI: 10.4171/RSMUP/130-5

Published online: 2013-12-30

On the Jump set of Solutions of the Total Variation Flow

Vicent Caselles, Khalid Jalalzai[1] and Matteo Novaga[2]

(1) Ecole Polytechnique, Palaiseau, France
(2) Università di Pisa, Italy

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

Keywords: Total variation flow, demonising model, nonlinear parabolic equations, functions of bounded variation

Caselles Vicent, Jalalzai Khalid, Novaga Matteo: On the Jump set of Solutions of the Total Variation Flow. Rend. Sem. Mat. Univ. Padova 130 (2013), 155-168. doi: 10.4171/RSMUP/130-5