Least gradient problem with respect to a non-strictly convex norm. (November 2020)

• Record Type: Journal Article
• Authors: Górny, Wojciech
• Is Part Of: Nonlinear analysis. Volume 200(2020)
• Publication Date: 2020-11
• Subjects: 35A15 -- 35J20 -- 49J10 -- 49J20; Least gradient problem -- Non-strict convexity -- Anisotropy; 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.2020.112049
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We study the planar least gradient problem with respect to an anisotropic norm for continuous boundary data. We prove existence of minimizers for strictly convex domains. Furthermore, we inspect the issue of uniqueness and regularity of minimizers only in terms of the modes of convexity of the norm and the domain. The results are independent from the regularity of the norm.