# Dirichlet boundary values on Euclidean balls with infinitely many solutions for the minimal surface system

## TL;DR

This paper extends Lawson-Osserman constructions to demonstrate that certain boundary conditions on Euclidean balls admit infinitely many solutions to the minimal surface system, including both smooth and nonsmooth solutions.

## Contribution

It introduces new boundary functions that lead to infinitely many analytic and nonsmooth solutions, revealing a novel phenomenon in minimal surface theory.

## Key findings

- Existence of boundary data with infinitely many solutions
- Presence of both smooth and nonsmooth solutions for the same boundary conditions
- Enrichment of Lawson-Osserman theory with new solution phenomena

## Abstract

We make systematic developments on Lawson-Osserman constructions relating to the Dirichlet problem (over unit disks) for minimal surfaces of high codimension in their 1977 Acta paper. In particular, we show the existence of boundary functions for which infinitely many analytic solutions and at least one nonsmooth Lipschitz solution exist simultaneously. This newly-discovered amusing phenomenon enriches the understanding on the Lawson-Osserman philosophy.