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

Matteo Focardi (), Francesco Geraci () and Emanuele Spadaro ()
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Matteo Focardi: Università degli Studi di Firenze
Francesco Geraci: Università degli Studi di Firenze
Emanuele Spadaro: Università di Roma “La Sapienza”

Journal of Optimization Theory and Applications, 2020, vol. 184, issue 1, No 7, 125-138

Abstract: 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.

Keywords: Classical obstacle problem; Free boundary; Monotonicity formulas; 35R35; 49N60 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10957-018-1398-y

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