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

Author

Listed:
  • Matteo Focardi

    (Università degli Studi di Firenze)

  • Francesco Geraci

    (Università degli Studi di Firenze)

  • Emanuele Spadaro

    (Università di Roma “La Sapienza”)

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.

Suggested Citation

  • Matteo Focardi & Francesco Geraci & Emanuele Spadaro, 2020. "Quasi-Monotonicity Formulas for Classical Obstacle Problems with Sobolev Coefficients and Applications," Journal of Optimization Theory and Applications, Springer, vol. 184(1), pages 125-138, January.
    • Handle: RePEc:spr:joptap:v:184:y:2020:i:1:d:10.1007_s10957-018-1398-y
    DOI: 10.1007/s10957-018-1398-y
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