Abstract
We prove, using direct variational arguments, an explicit energy-treshold criterion for regular points of 2-dimensional Mumford-Shah energy minimizers. From this we infer an explicit constant for the density lower bound of De Giorgi, Carriero and Leaci.
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Lellis, C.D., Focardi, M. Density lower bound estimates for local minimizers of the 2d Mumford–Shah energy. manuscripta math. 142, 215–232 (2013). https://doi.org/10.1007/s00229-012-0601-y
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DOI: https://doi.org/10.1007/s00229-012-0601-y