Long time existence and uniqueness of solutions to the Yang-Mills heat equation is proven over a compact 3-manifold with smooth boundary. The initial data is taken to be a Lie algebra valued connection form in the Sobolev ...

Lommel's function s μ,ν(z) is a particular solution of the differential equation z 2y″ + zy′ + (z 2 - ν 2)y = z μ+1. Here we present estimates and monotonicity properties of the positive zeros of s μ-1/2,1/2(z) when μ ∈ ...