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

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.

arXiv comment24 pages; To appear in the Journal of Mathematical Analysis and Applications

References in corpus (2)

• Solving Poisson's equation for the standard weighted Laplacian in the unit disc
• On the Lipschitz continuity of certain quasiregular mappings between smooth Jordan domains