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European Mathematical Society Publishing House
2016-09-19 17:05:49
Rendiconti del Seminario Matematico della Università di Padova
Rend. Sem. Mat. Univ. Padova
RSMUP
0041-8994
2240-2926
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10.4171/RSMUP
http://www.ems-ph.org/doi/10.4171/RSMUP
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130
2013
0
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, PISA, ITALY
Total variation flow, demonising model, nonlinear parabolic equations, functions of bounded variation
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.
Partial differential equations
Real functions
Computer science
Information and communication, circuits
155
168
10.4171/RSMUP/130-5
http://www.ems-ph.org/doi/10.4171/RSMUP/130-5