The trace space of anisotropic least gradient functions depends on the anisotropy

DOI10.1007/s00208-022-02488-4zbMath1526.35178arXiv2202.00139OpenAlexW4303615210MaRDI QIDQ6084198

Wojciech Górny

Publication date: 31 October 2023

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2202.00139

zbMATH Keywords

Dirichlet problemleast gradient functions

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Methods involving semicontinuity and convergence; relaxation (49J45) Boundary values of solutions to elliptic equations and elliptic systems (35J67) Singular elliptic equations (35J75)

Cites Work

• The Euler-Lagrange equation for the anisotropic least gradient problem
• Special cases of the planar least gradient problem
• Planar least gradient problem: existence, regularity and anisotropic case
• Existence and uniqueness of minimizers of general least gradient problems
• \(L^p\) bounds for boundary-to-boundary transport densities, and \(W^{1,p}\) bounds for the BV least gradient problem in 2D
• A notion of total variation depending on a metric with discontinuous coefficients
• Comportamento delle successioni convergenti di frontiere minimali
• Minimal cones and the Bernstein problem
• The planar least gradient problem in convex domains: the discontinuous case
• Functions of least gradient and 1-harmonic functions
• Characteristic functions on the boundary of a planar domain need not be traces of least gradient functions
• Existence and structure of minimizers of least gradient problems
• 𝐿^{𝑝} regularity of least gradient functions
• Existence of minimisers in the least gradient problem for general boundary data
• Not all traces on the circle come from functions of least gradient in the disk
• Non-locality, non-linearity, and existence of solutions to the Dirichlet problem for least gradient functions in metric measure spaces
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