#### Vol. 307, No. 1, 2020

 Recent Issues Vol. 317: 1 Vol. 316: 1  2 Vol. 315: 1  2 Vol. 314: 1  2 Vol. 313: 1  2 Vol. 312: 1  2 Vol. 311: 1  2 Vol. 310: 1  2 Online Archive Volume: Issue:
 The Journal Subscriptions Editorial Board Officers Contacts Submission Guidelines Submission Form Policies for Authors ISSN: 1945-5844 (e-only) ISSN: 0030-8730 (print) Special Issues Author Index To Appear Other MSP Journals
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

Vol. 307 (2020), No. 1, 1–12
##### Abstract

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 ${C}^{2}$ 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.

##### Keywords
Dirichlet problem for minimal hypersurface equation, Lipschitz continuous boundary data
Primary: 53C21
Secondary: 58J05