Invertibility criteria for the biharmonic single-layer potential

TL;DR

This paper establishes simple sufficient conditions for the invertibility of the biharmonic single-layer potential operator, addressing a gap in understanding compared to the Laplacian case.

Contribution

It introduces new criteria that guarantee invertibility of the biharmonic single-layer operator across various problems, advancing theoretical understanding.

Findings

Provided simple sufficient conditions for invertibility

Addressed invertibility issues related to degenerate scales

Extended understanding from Laplacian to Bilaplacian operators

Abstract

While the single-layer operator for the Laplacian is well understood, questions remain concerning the single-layer operator for the Bilaplacian, particularly with regard to invertibility issues linked with degenerate scales. In this article, we provide simple sufficient conditions ensuring this invertibility for a wide range of problems.