We develop the complete free boundary analysis for solutions to classical obstacle problems related to nondegenerate nonlinear variational energies. The key tools are optimal C1,1 regularity, which we review more generally for solutions to variational inequalities driven by nonlinear coercive smooth vector fields, and the results in {FocGelSp15} concerning the obstacle problem for quadratic energies with Lipschitz coefficients. Furthermore, we highlight similar conclusions for locally coercive vector fields having in mind applications to the area functional, or more generally to area-type functionals, as well.

The classical obstacle problem for nonlinear variational energies / Focardi, Matteo; Geraci, Francesco; Spadaro, EMANUELE NUNZIO. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 154:(2017), pp. 71-87. [10.1016/j.na.2016.10.020]

The classical obstacle problem for nonlinear variational energies

Emanuele Spadaro
2017

Abstract

We develop the complete free boundary analysis for solutions to classical obstacle problems related to nondegenerate nonlinear variational energies. The key tools are optimal C1,1 regularity, which we review more generally for solutions to variational inequalities driven by nonlinear coercive smooth vector fields, and the results in {FocGelSp15} concerning the obstacle problem for quadratic energies with Lipschitz coefficients. Furthermore, we highlight similar conclusions for locally coercive vector fields having in mind applications to the area functional, or more generally to area-type functionals, as well.
2017
nonlinear obstacle problem
01 Pubblicazione su rivista::01a Articolo in rivista
The classical obstacle problem for nonlinear variational energies / Focardi, Matteo; Geraci, Francesco; Spadaro, EMANUELE NUNZIO. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 154:(2017), pp. 71-87. [10.1016/j.na.2016.10.020]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1117464
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