Special Session 4: Mathematical methods in electromagnetism and related topics

Nonvariational solutions of boundary value problems for the Helmholtz equation in multiply connected domains
Massimo Lanza de Cristoforis
Dipartimento di Matematica `Tullio Levi-Civita`
Italy
Co-Author(s):    
Abstract:
We consider a possibly multiply connected bounded open subset $\Omega$ of ${\mathbb{R}}^n$ of class $C^{1,\alpha}$, $\alpha\in]0,1[$ and we plan to solve classical boundary value problems for the Helmholtz equation in $\Omega$ and in the exterior of $\Omega$ in terms of acoustic layer potentials. The main focus of the talk is on $\alpha$-H\{o}lder continuous solutions which may not have a classical normal derivative at the boundary points of $\Omega$ and that may have an infinite Dirichlet integral around the boundary of $\Omega$. Namely for solutions that do not belong to the classical variational setting.