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

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

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 obstac...

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Veröffentlicht in:Journal of optimization theory and applications 2020, Vol.184 (1), p.125-138
Hauptverfasser: Focardi, Matteo, Geraci, Francesco, Spadaro, Emanuele
Format: Artikel
Sprache:eng
Schlagworte:
Applications of Mathematics
Calculus of Variations and Optimal Control
Optimization
Engineering
Free boundaries
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Sobolev space
Theory of Computation
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Zusammenfassung: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.
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-018-1398-y