# Weak maximum principle for biharmonic equations in quasiconvex Lipschitz domains

## TL;DR

This paper proves the weak maximum principle for biharmonic equations in higher-dimensional quasiconvex Lipschitz domains, extending known results from convex and $C^1$ domains to a broader class.

## Contribution

It establishes the weak maximum principle in quasiconvex Lipschitz domains in higher dimensions, a sharp condition that generalizes previous results.

## Key findings

- Weak maximum principle holds in quasiconvex Lipschitz domains in dimensions greater than three.
- The result recovers the validity in convex and $C^1$ domains.
- Provides a sharp condition for the maximum principle in Lipschitz domains.

## Abstract

In dimension two or three, the weak maximum principal for biharmonic equation is valid in any bounded Lipschitz domains. In higher dimensions (greater than three), it was only known that the weak maximum principle holds in convex domains or $C^1$ domains, and may fail in general Lipschitz domains. In this paper, we prove the weak maximum principle in higher dimensions in quasiconvex Lipschitz domains, which is a sharp condition in some sense and recovers both convex and $C^1$ domains.