Abstract
The goal of this paper is to reconsider the classical elliptic system rot v = f, div v = g in simply connected domains with bounded connected boundaries (bounded and exterior sets). The main result shows solvability of the problem in the maximal regularity regime in the L (p) -framework taking into account the optimal/minimal requirements on the smoothness of the boundary.
A generalization for the Besov spaces is studied, too, for for. As a limit case we prove the result for , provided the boundary is merely in.
The dimension three is distinguished due to the physical interpretation of the system. In other words we revised and extended the classical results of Friedrichs (Commun Pure Appl Math 8;551-590, 1955) and Solonnikov (Zap Nauch Sem LOMI 21:112-158, 1971).