Representation formula and bi-Lipschitz continuity of solutions to inhomogeneous biharmonic Dirichlet problems in the unit disk

TL;DR

This paper derives a representation formula and proves bi-Lipschitz continuity for solutions to inhomogeneous biharmonic Dirichlet problems in the unit disk, enhancing understanding of their structure and regularity.

Contribution

It introduces a new representation formula and establishes bi-Lipschitz continuity for solutions, providing novel insights into the regularity of biharmonic problems.

Findings

Representation formula for solutions

Uniqueness of solutions established

Bi-Lipschitz continuity proved

Abstract

The aim of this paper is twofold. First, we establish the representation formula and the uniqueness of the solutions to a class of inhomogeneous biharmonic Dirichlet problems, and then prove the bi-Lipschitz continuity of the solutions.