The planar least gradient problem in convex domains, the case of continuous datum

DOI10.1016/j.na.2021.112595zbMath1476.49002arXiv1911.08403OpenAlexW3207300914MaRDI QIDQ2238808

Ahmad Sabra, Piotr Rybka

Publication date: 2 November 2021

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1911.08403

zbMATH Keywords

\textit{BV} functionsconvex but not strictly convex domainsleast gradienttrace solutions

Mathematics Subject Classification ID

Nonsmooth analysis (49J52) Variational problems in a geometric measure-theoretic setting (49Q20) Existence theories for free problems in two or more independent variables (49J10) Optimization of shapes other than minimal surfaces (49Q10)

Related Items (6)

Least gradient problem on annuli ⋮ \( W^{1, p}\) regularity on the solution of the BV least gradient problem with Dirichlet condition on a part of the boundary ⋮ Applications of optimal transport methods in the least gradient problem ⋮ Optimal Transport Approach to Sobolev Regularity of Solutions to the Weighted Least Gradient Problem ⋮ Least gradient problem with Dirichlet condition imposed on a part of the boundary ⋮ Non-locality, non-linearity, and existence of solutions to the Dirichlet problem for least gradient functions in metric measure spaces

Cites Work

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• \(L^p\) bounds for boundary-to-boundary transport densities, and \(W^{1,p}\) bounds for the BV least gradient problem in 2D
• (Non)uniqueness of minimizers in the least gradient problem
• Comportamento delle successioni convergenti di frontiere minimali
• The planar least gradient problem in convex domains: the discontinuous case
• Functions of least gradient and 1-harmonic functions
• Existence and structure of minimizers of least gradient problems
• Not all traces on the circle come from functions of least gradient in the disk
• A Weighted Minimum Gradient Problem with Complete Electrode Model Boundary Conditions for Conductivity Imaging

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