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

## TL;DR

This paper investigates the quasisuperminimizing constant for the minimum of two such functions in higher dimensions, extending previous one-dimensional results and exploring cases with different constants.

## Contribution

It provides higher-dimensional examples and analyzes the case where the two functions have different quasisuperminimizing constants.

## Key findings

- Higher-dimensional examples of quasisuperminimizers are constructed.
- The quasisuperminimizing constant for the minimum is shown to be close to optimal.
- The case with different constants for the two functions is analyzed.

## Abstract

It was shown in Bj\"orn--Bj\"orn--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.