Oblique derivative and interface problems on polygonal domains and networks

Abstract

We Investigate oblique derivative problems associated to the Laplace operator on a polygon and we extend our study to "polygonal interface problems" which are an extension to networks of the prevlous ones. We focus on the non variational character of such problems. We obtain index formulae, a calculus of the dimension of the kernel, an expansion of the 'semi-variational" (or weak) solutions into regular and singular parts and formulae for the coefficients of the singularities In such expanslons.