The quasisuperminimizing constant for the minimum of two quasisuperminimizers in R^n

Abstract

It was shown in Björn--Björn--Korte ("Minima of quasisuperminimizers", Nonlinear Anal. 155 (2017), 264-284) that $u:=\min \{u_1,u_2\}$ is a $\overline{Q}$-quasisuperminimizer if $u_1$ and $u_2$ are $Q$-quasisuperminimizers and $\overline{Q}=2Q^2/(Q+1)$. Moreover, one-dimensional examples therein show that $\overline{Q}$ is close to optimal. In this paper we give similar examples in higher dimensions. The case when $u_1$ and $u_2$ have different quasisuperminimizing constants is considered as well.