C^{1,alpha}theory for the prescribed mean curvature equation with Dirichlet data

Bourni, Theodora

doi:10.1007/s12220-010-9176-6

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C^{1,alpha}theory for the prescribed mean curvature equation with Dirichlet data

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Bourni, Theodora
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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1007.3402
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Citation

Bourni, T. (2008). C^{1,alpha}theory for the prescribed mean curvature equation with Dirichlet data. The Journal of Geometric Analysis. doi:10.1007/s12220-010-9176-6.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0012-C6C5-C

Abstract

In this work we study solutions of the prescribed mean curvature equation over a general domain that do not necessarily attain the given boundary data. To such a solution, we can naturally associate a current with support in the closed cylinder above the domain and with boundary given by the prescribed boundary data and which inherits a natural minimizing property. Our main result is that its support is a $C^{1,\alpha}$ manifold-with-boundary, with boundary equal to the prescribed boundary data, provided that both the initial domain and the prescribed boundary data are of class C^{1,\alpha}.