Regularity of minimal surfaces with lower-dimensional obstacles

DOI10.1515/crelle-2019-0035zbMath1454.49038arXiv1802.07607OpenAlexW2988211454MaRDI QIDQ2209449

Joaquim Serra, Xavier Fernández-Real

Publication date: 2 November 2020

Published in: Journal für die Reine und Angewandte Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1802.07607

zbMATH Keywords

Plateau problemthin obstacleregularity for minimal surfaces

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Variational problems concerning minimal surfaces (problems in two independent variables) (58E12)

Related Items (3)

Regularity of solutions to nonlinear thin and boundary obstacle problems ⋮ How a minimal surface leaves a thin obstacle ⋮ The thin obstacle problem: a survey

Cites Work

• How a minimal surface leaves an obstacle
• Regularity of a minimal boundary with a thin obstacle
• The regularity of free boundaries in higher dimensions
• The obstacle problem revisited
• An elementary regularity theory of minimal surfaces
• Regularity of flat level sets in phase transitions
• Minimal varieties in Riemannian manifolds
• Minimal cones and the Bernstein problem
• The regularity of minimal surfaces defined over slit domains
• Non-parametric minimal surfaces with discontinuous and thin obstacles
• Optimal regularity of lower dimensional obstacle problems
• The structure of the free boundary for lower dimensional obstacle problems
• Further regularity for the signorini problem
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