Reflection principle for quasiminimizers

Abstract

It is shown that the reflection principle holds for $K$--quasiminimizers in $\mathbb{R}^n$, $n \geq 2$, provided that $K \in [1, 2)$. For $n = 1$ the principle holds for all $K \geq 1$ and an example shows that $K$ is not preserved in the reflection process. A local integrability result up to the boundary is proved for the derivative of a quasiminimizer in $\mathbb{R}^n$, $n \geq 1$; the result is needed for the reflection principle.