Let Ω be a bounded piecewise regular open set with convex corners, and let MS(u) be the Mumford-Shah functional on the space SBV(Ω). We prove that the elastic minimizer of MS is a local minimizer with respect to the L1-topology. This is obtained as an application of interior and boundary monotonicity formulas for a weak notion of quasiminimizers of the Mumford-Shah energy. The local minimality result is then extended to more general free discontinuity problems taking into account also boundary conditions.
Local minimality results for the mumford-shah functional via monotonicity
Giacomini A.
2020-01-01
Abstract
Let Ω be a bounded piecewise regular open set with convex corners, and let MS(u) be the Mumford-Shah functional on the space SBV(Ω). We prove that the elastic minimizer of MS is a local minimizer with respect to the L1-topology. This is obtained as an application of interior and boundary monotonicity formulas for a weak notion of quasiminimizers of the Mumford-Shah energy. The local minimality result is then extended to more general free discontinuity problems taking into account also boundary conditions.File in questo prodotto:
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