The classical obstacle problem for nonlinear variational energies. (May 2017)

• Record Type: Journal Article
• Authors: Focardi, M.; Geraci, F.; Spadaro, E.
• Is Part Of: Nonlinear analysis. Volume 154(2017)
• Page Start: 71
• Page End: 87
• Publication Date: 2017-05
• Subjects: 35R35 -- 35R45 -- 49N60; Variational inequalities -- Free boundary problems -- Regularity; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2016.10.020
• Languages: English
• ISSNs: 0362-546X

Abstract

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 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 Focardi et al. (2015) 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.