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Quasi-Monotonicity Formulas for Classical Obstacle Problems with Sobolev Coefficients and Applications

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Abstract

We establish Weiss’ and Monneau’s type quasi-monotonicity formulas for quadratic energies having matrix of coefficients in a Sobolev space with summability exponent larger than the space dimension and provide an application to the corresponding free boundary analysis for the related classical obstacle problems.

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Acknowledgements

Emanuele Spadaro has been supported by the ERC-STG Grant No. 759229 HiCoS “Higher Co-dimension Singularities: Minimal Surfaces and the Thin Obstacle Problem.” Matteo Focardi, Francesco Geraci, Emanuele Spadaro are members of 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. DiMaI, Università degli Studi di Firenze, Viale Morgagni 67/A, 50134, Firenze, Italy

    Matteo Focardi & Francesco Geraci

  2. Università di Roma “La Sapienza”, P.le Aldo Moro 5, Roma, Italy

    Emanuele Spadaro

Authors
  1. Matteo Focardi
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  2. Francesco Geraci
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  3. Emanuele Spadaro
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Correspondence to Matteo Focardi.

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Focardi, M., Geraci, F. & Spadaro, E. Quasi-Monotonicity Formulas for Classical Obstacle Problems with Sobolev Coefficients and Applications. J Optim Theory Appl 184, 125–138 (2020). https://doi.org/10.1007/s10957-018-1398-y

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  • DOI: https://doi.org/10.1007/s10957-018-1398-y

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