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Archiv der Mathematik

, Volume 112, Issue 2, pp 213–222 | Cite as

The Dirichlet problem for the \(\alpha \)-singular minimal surface equation

  • Rafael LópezEmail author
Article
  • 15 Downloads

Abstract

Let \(\Omega \subset \mathbb {R}^n\) be a bounded mean convex domain. If \(\alpha <0\), we prove the existence and uniqueness of classical solutions of the Dirichlet problem in \(\Omega \) for the \(\alpha \)-singular minimal surface equation with arbitrary continuous boundary data.

Keywords

Dirichlet problem Singular minimal surface Method of continuity A priori estimates 

Mathematics Subject Classification

35J60 53A10 53C42 

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Departamento de Geometría y Topología, Instituto de Matemáticas (IEMath-GR)Universidad de GranadaGranadaSpain

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