Regularity for obstacle problems without structure conditions. (December 2021)

• Record Type: Journal Article
• Authors: Bertazzoni, Giacomo; Riccò, Samuele
• Is Part Of: Nonlinear analysis. Volume 62(2021)
• Publication Date: 2021-12
• Subjects: Lipschitz regularity results -- p–q growth conditions -- Obstacle problem -- Lavrentiev phenomenon -- a-priori estimates; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2021.103353
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: This paper deals with the Lipschitz regularity of minimizers for a class of variational obstacle problems with possible occurrence of the Lavrentiev phenomenon. In order to overcome this problem, the availment of the notions of relaxed functional and Lavrentiev gap is needed. The main tool used here is a crucial Lemma which reveals to be needed because it allows us to move from the variational obstacle problem to the relaxed-functional-related one. This is fundamental in order to find the solutions' regularity that we intended to study. We assume the same Sobolev regularity both for the gradient of the obstacle and for the coefficients.