The classical obstacle problem with Hölder continuous coefficients. (January 2023)

• Record Type: Journal Article
• Authors: Andreucci, Giovanna; Focardi, Matteo
• Is Part Of: Nonlinear analysis. Volume 226(2023)
• Publication Date: 2023-01
• Subjects: primary 35R35 49N60; Classical obstacle problem -- Free boundary -- Monotonicity formulas; 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.2022.113139
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: Weiss' and Monneau's type quasi-monotonicity formulas are established for quadratic energies having matrix of coefficients which are Dini, double-Dini continuous, respectively. Free boundary regularity for the corresponding classical obstacle problems under Hölder continuity assumptions is then deduced.