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

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.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-0012-C6C5-C Version Permalink: https://hdl.handle.net/11858/00-001M-0000-0012-C6C9-4
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1007.3402 (Preprint), 495KB
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 Creators:
Bourni, Theodora1, Author           
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1Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, Golm, DE, ou_24012              

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Free keywords: Mathematics, Differential Geometry, math.DG,Mathematics, Analysis of PDEs, math.AP,
 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}.

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 Dates: 2010-07-2020112008-09
 Publication Status: Published online
 Pages: 45 pages, no figures, to appear in Journal of Geometric Analysis
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 Rev. Type: -
 Identifiers: arXiv: 1007.3402
URI: http://arxiv.org/abs/1007.3402
DOI: 10.1007/s12220-010-9176-6
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Title: The Journal of Geometric Analysis
Source Genre: Journal
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Publ. Info: Boca Raton, FL : CRC Press
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: - Identifier: ISSN: 1050-6926
CoNE: https://pure.mpg.de/cone/journals/resource/954926996194_1