Regularity results for a class of non-differentiable obstacle problems. (May 2020)

• Record Type: Journal Article
• Authors: Eleuteri, Michela; Passarelli di Napoli, Antonia
• Is Part Of: Nonlinear analysis. Volume 194(2020)
• Publication Date: 2020-05
• Subjects: 26A27 -- 49J40 -- 47J20; Non-differentiability -- Obstacle problems -- Higher differentiability; 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.2019.01.024
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper we prove the higher differentiability in the scale of Besov spaces of the solutions to a class of obstacle problems of the type min ∫ Ω F ( x, z, D z ) : z ∈ K ψ ( Ω ) . Here Ω is an open bounded set of R n, n ≥ 2, ψ is a fixed function called obstacle and K ψ ( Ω ) is set of admissible functions z ∈ W 1, p ( Ω ) such that z ≥ ψ a.e. in Ω . We assume that the gradient of the obstacle belongs to a suitable Besov space. The main novelty here is that we are not assuming any differentiability on the partial maps x ↦ F ( x, z, D z ) and z ↦ F ( x, z, D z ), but only their Hölder continuity.