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The Dirichlet problem
for the mimimal hypersurface equation with Lipschitz
continuous boundary data in a Riemannian manifold
Arì Aiolfi, Giovanni da Silva Nunes, Lisandra Sauer and Rodrigo Soares |
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Vol. 307 (2020), No. 1, 1–12
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Abstract |
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In Corollary 1 of J. Reine Angew. Math. 354:123–140 (1984), G. H. Williams proves the existence of solutions to the Dirichlet problem for the minimal hypersurface equation on arbitrary bounded domains of the Euclidean space for Lipschitz continuous boundary data with optimal Lipschitz constant. We prove a similar result on a complete Riemannian manifold. Our theorem recovers Williams’ Corollary 1 when the ambient is the Euclidean space. Moreover, it applies to unbounded domains. |
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Keywords
Dirichlet problem for minimal hypersurface equation,
Lipschitz continuous boundary data
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Mathematical Subject Classification 2010
Primary: 53C21
Secondary: 58J05
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Milestones
Received: 11 September 2018
Revised: 27 January 2020
Accepted: 27 March 2020
Published: 8 August 2020
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Authors |
| Arì Aiolfi | |
| Departamento de Matemática Universidade Federal de Santa Maria Santa Maria Brazil |
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| Giovanni da Silva Nunes | |
| Instituto de Física e
Matemática Universidade Federal de Pelotas Pelotas Brazil |
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| Lisandra Sauer | |
| Instituto de Física e
Matemática Universidade Federal de Pelotas Pelotas Brazil |
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| Rodrigo Soares | |
| Instituto de Matemática e
Estatística Universidade Federal do Rio Grande Rio Grande Brazil |
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