Solving exterior Neumann boundary value problems for Beltrami fields through the Beltrami system (Q548785)

The eigenfunctions of \(\mathrm{curl}\) for eigenvalues \(\kappa\in\mathbb{R}\setminus\left\{ 0\right\} \) are known as Beltrami fields and are studied here for exterior domains with the boundary condition of prescribed normal components. For an extended elliptic system (extended Beltrami system) the corresponding boundary value problem is studied via the integral equation method. A suitable Silver-Müller-type radiation condition is derived and unique solvability is demonstrated for radiation boundary value problems. The approach avoids having to exclude any exceptional values for \(\kappa\). The solution theory of the extended system implies, under suitable constraints, the unique solvability of the Beltrami field boundary value problem.