The regularity of Euclidean Lipschitz boundaries with prescribed mean curvature in three-dimensional contact sub-Riemannian manifolds. (May 2016)

• Record Type: Journal Article
• Authors: Galli, Matteo
• Is Part Of: Nonlinear analysis. Volume 136(2016)
• Page Start: 40
• Page End: 50
• Publication Date: 2016-05
• Subjects: 53C17 -- 49Q20; Sub-Riemannian geometry -- Contact manifolds -- Geometric variational problems -- Minimal surfaces -- Prescribed mean curvature surfaces -- Heisenberg group; 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.2016.02.009
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper we consider a set E ⊂ Ω with prescribed mean curvature f ∈ C ( Ω ) and Euclidean Lipschitz boundary ∂ E = Σ inside a three-dimensional contact sub-Riemannian manifold M . We prove that if Σ is locally a regular intrinsic graph, the characteristic curves are of class C 2 . The result is shape and improves the ones contained in Capogna et al. (2009) and Galli and Ritoré (2015).