Monotonicity formulas for obstacle problems with Lipschitz coefficients

  • M. FocardiEmail author
  • M. S. Gelli
  • E. Spadaro


We prove quasi-monotonicity formulas for classical obstacle-type problems with energies being the sum of a quadratic form with Lipschitz coefficients, and a Hölder continuous linear term. With the help of those formulas we are able to carry out the full analysis of the regularity of free-boundary points following the approaches by Caffarelli (J Fourier Anal Appl 4(4–5), 383–402, 1998), Monneau (J Geom Anal 13(2), 359–389, 2003), and Weiss (Invent Math 138(1), 23–50, 1999).

Mathematics Subject Classification

35R35 49N60 



The first two authors have been supported by the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM).


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Authors and Affiliations

  1. 1.DiMaI “U. Dini”Università di FirenzeFlorenceItaly
  2. 2.Dipartimento di MatematicaUniversità di PisaPisaItaly
  3. 3.Max-Planck-Institut für Mathematik in den NaturwissenschaftenLeipzigGermany

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