On the fine regularity of the singular set in the nonlinear obstacle problem. (May 2022)

• Record Type: Journal Article
• Authors: Savin, Ovidiu; Yu, Hui
• Is Part Of: Nonlinear analysis. Volume 218(2022)
• Publication Date: 2022-05
• Subjects: Free boundary -- Obstacle problem -- Singular set; 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.2021.112770
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We revisit and sharpen the results from our previous work, where we investigated the regularity of the singular set of the free boundary in the nonlinear obstacle problem. As in the work of Figalli–Serra on the classical obstacle problem, we show that each stratum can be further decomposed into a 'good' part and an 'anomalous' part, where the former is covered by C 1, 1 − manifolds, and the latter is of lower dimension.