On the curvature of free boundaries with a Bernoulli-type condition Original Research Article

In this paper we study the classical external Bernoulli problem set in an annular domain ΩΩ of the plane. We focus on the curvature of the free boundary ΓΓ (outer component of the boundary of our domain) and establish a one-to-one correspondence between positive/negative curvature arcs of ΓΓ and of the curve γγ representing the data, extending a method put forward by A. Acker. Moreover we show that the positive curvature arcs on the free boundary bend less than the corresponding arcs on the inner curve, i.e. the maximum attained by the curvature is greater on γγ than on ΓΓ. Thus we can draw the following conclusions: the geometry of ΓΓ is simpler than that of γγ (an already known result); the shape of ΓΓ is alleviated with respect to that of γγ.