We prove the optimal $ C^{1, 1} $ regularity for minimizers of the prescribed mean curvature
functional over isotopy classes. As an application, we find an embedded sphere of …

We provide an elementary proof of the $ C^{1, 1} $-regularity for $ C^{1,\alpha} $($\alpha\in
(0, 1) $) solutions to the multiple membrane problem of the same divergence form. This …

Energy-minimizing constraint maps are a natural extension of the obstacle problem within a
vectorial framework. Due to inherent topological constraints, these maps manifest a diverse …

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Free boundary regularity in the multiple membrane problem in the plane Skip to content Should
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Abstract We study the Two Membranes Problem for fully nonlinear operators both in the
local (second order) and nonlocal setting. The problem arises when studying a" bid an ask" …

We investigate the regularity of the free boundaries in the 3 elastic membranes problem. We
show that the two free boundaries corresponding to the coincidence regions between …

Questions about the existence of minimal submanifolds in compact Riemannian manifolds
occupy a prominent place in the theory of geometric variational problems, and have been …