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arXiv · 1709.08092

The Dirichlet problem for the minimal hypersurface equation with Lipschitz continuous boundary data on domains of a Riemannian manifold

Ari J. Aiolfi·Giovanni Nunes·Lisandra Sauer·Rodrigo B. Soares
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Abstract

Given a C2-domain with compact boundary in an arbitrary complete Riemannian manifold, we search for smallness conditions on the boundary data for which the Dirichlet problem for the minimal hypersurface equation is solvable. We obtain an extension to Riemannian manifolds of an existence result of G. H. Williams ( J. Reine Angew. Math. 354:123-140, 1984).

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Ari J. Aiolfi, Giovanni Nunes, Lisandra Sauer, Rodrigo B. Soares. 2017-09-23. The Dirichlet problem for the minimal hypersurface equation with Lipschitz continuous boundary data on domains of a Riemannian manifold. https://arxiv.org/abs/1709.08092

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