Calculus of Variations and Geometric Measure Theory
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M. Focardi - F. Geraci - E. Spadaro

The classical obstacle problem for nonlinear variational energies

created by focardi on 31 Oct 2016


Nonlinear Analysis TMA

Inserted: 31 oct 2016
Last Updated: 31 oct 2016

Year: 2016


We develop the complete free boundary analysis for solutions to classical obstacle problems related to nondegenerate nonlinear variational energies. The key tools are optimal $C^{1,1}$ regularity, which we review more generally for solutions to variational inequalities driven by nonlinear coercive smooth vector fields, and the results in \cite{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.


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