The ∂̄-Neumann problem and boundary integral equations

Abstract

In this paper, we find an equivalent boundary integral equation to the classical [Formula: see text]-Neumann problem. The new equation contains an equivalent regularity to the global regularity of the [Formula: see text]-Neumann problem. We also use the integral equations to observe a new-found rigidity property of the [Formula: see text]-Neumann problem on the unit ball in [Formula: see text].