Improved C^1,1 regularity for multiple membranes problem

2023/07/31 by Zhichao Wang, Xin Zhou, Wang, Zhichao +1
Computer Science · Engineering · Mathematics · #Analysis of PDEs (math.AP) #Complexity and Algorithms in Graphs #Differential Geometry (math.DG) #Extraction and Separation Processes #FOS: Mathematics #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2308.00172

openalex publication_date 2023/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the C^1,1-regularity for stationary C^1,α (α∈(0,1)) solutions to the multiple membrane problem. This regularity estimate was essentially used in our recent work on Yau's four minimal spheres conjecture.

Related

• On the multiple membranes problem
• Free boundary regularity in the multiple membrane problem in the plane
• C^{1, 1} regularity for solutions to the degenerate L_p Dual Minkowski problem
• Free boundary regularity in the triple membrane problem
• Weak uniqueness and partial regularity for the composite membrane problem