On the non-existence of solutions of the Dirichlet problem for the minimal surface system

TL;DR

This paper investigates conditions under which solutions to the Dirichlet problem for minimal surface systems of codimension two or higher do not exist, even with irregular boundary domains.

Contribution

It provides new non-existence results for minimal surface systems in higher codimensions, expanding understanding of boundary regularity effects.

Findings

Non-existence of solutions in certain higher codimension cases

Results hold even with non-$C^1$ boundary domains

Extends previous non-existence theorems to broader settings

Abstract

In this paper we study the non-existence of solutions to the Dirichlet problem for minimal graphs of codimension $\geq 2$, including certain situations over domain $\Omega$ even with non-$C^1$ boundary $\partial \Omega$.