Manuscripta Mathematica

, Volume 142, Issue 1–2, pp 215–232 | Cite as

Density lower bound estimates for local minimizers of the 2d Mumford–Shah energy

  • Camillo De Lellis
  • Matteo FocardiEmail author


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.


Radon Measure Admissible Function Monotonicity Formula Perforated Domain Dirichlet Energy 
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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Institut für MathematikUniversität ZürichZürichSwitzerland
  2. 2.Dipartimento di Matematica “U. Dini”Università di FirenzeFirenzeItaly

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