Qualitative properties of the boundary derivative of the capacity potential for special classes of annular domains

Abstract

AbstractLet U(p) denote the capacity potential in an annular domain Ω (bounded by Jordan curves). We describe the qualitative behavior of ∥Δ∥ on the line segments of ∂Ω which are arbitrary, radial, or ν‐directional (for some vector ν ≠ 0) in the respective cases where Ω is a convex, starlike, or ≠‐convex annular domain. We apply these results to some free‐boundary extremal problems in which the capacity plus weighted area functional is minimized in restricted classes of annular domains Ω.