AbstractLetU(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
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