The Euler–Lagrange equation for the Anisotropic least gradient problem. (October 2016)

• Record Type: Journal Article
• Authors: Mazón, José M.
• Is Part Of: Nonlinear analysis. Volume 31(2016)
• Page Start: 452
• Page End: 472
• Publication Date: 2016-10
• Subjects: Functions of least gradient -- Conductivity imaging problem -- Anisotropy total variation; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2016.02.009
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper we find the Euler–Lagrange equation for the anisotropic least gradient problem inf { ∫ Ω ϕ ( x, D u ) : u ∈ B V ( Ω ), u | ∂ Ω = f } being ϕ a metric integrand and f ∈ L 1 ( ∂ Ω ) . We also characterize the functions of ϕ -least gradient as those whose boundary of the level set is ϕ -area minimizing in Ω .