On the singular planar Plateau problem

DOI10.1007/S00526-024-02853-YMaRDI QIDQ6641643

M. Caroccia, Riccardo Scala

Publication date: 21 November 2024

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Methods involving semicontinuity and convergence; relaxation (49J45) Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Length, area, volume, other geometric measure theory (28A75)

Cites Work

• Title not available (Why is that?)
• Intrinsic structure of minimal discs in metric spaces
• The Plateau-Douglas problem for singular configurations and in general metric spaces
• Sets of finite perimeter and geometric variational problems. An introduction to geometric measure theory
• SINGULAR CURVES AND THE PLATEAU PROBLEM
• The relaxed area of 𝕊¹-valued singular maps in the strict BV-convergence
• Optimal estimates for the triple junction function and other surprising aspects of the area functional
• Plateau's problem for singular curves
• Relaxed area of graphs of piecewise Lipschitz maps in the strict \(BV\)-convergence
• Relaxed area of 0-homogeneous maps in the strict \textit{BV}-convergence
• Upper bounds for the relaxed area of \(\mathbb{S}^1\)-valued Sobolev maps and its countably subadditive interior envelope

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