Improved $C^{1,1}$ Regularity for Multiple Membranes Problem

Abstract

We prove the $C^{1,1}$-regularity for stationary $C^{1,\alpha }$ ($\alpha \in (0,1)$) solutions to the multiple membrane problem. This regularity estimate was essentially used in our recent work on Yau’s four minimal spheres conjecture [arXiv:2305.08755].

Keywords

Multiple membranes / Optimal regularity / Prescribed mean curvature / Multiplicity / Elliptic operators

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Peking University