An estimate concerning the difference between minimizer and boundary value in some polyconvex problems. (February 2022)

• Record Type: Journal Article
• Authors: Colucci, Renato; Leonetti, Francesco; Treu, Giulia
• Is Part Of: Nonlinear analysis. Volume 215(2022)
• Publication Date: 2022-02
• Subjects: 49N60 -- 35B65; Regularity -- Minimizer -- Polyconvex -- Functional -- Non standard -- Growth; 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.2021.112635
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: This paper is concerned with regularity of minimizers of integral functionals with polyconvex potentials. In particular we obtain bounds on the difference | u − u ∗ | ∞ for minimizers u : Ω ⊂ R 3 → R 3 of problem min ∫ Ω f ( x, D v ( x ) ) d x, v ∈ u ∗ + W 0 1, p ( Ω, R 3 ) .