On the geometric form of free boundaries satisfying a bernoulli condition
Andrew F. Acker, Lawrence Edward Payne · Mathematical Methods in the Applied Sciences · 1984
Abstract In the x–y plane, let Ω denote an annular domain bounded by the simple closed curves ⌜ and ⌜ * , such that the capacity potential U in Ω satisfies ∣ ▽ U ∣ = 1 on ⌜. Assuming ⌜ * to be known, we obtain qualitative properties of ⌜. For example, the number of local maxima or minima of the y ‐co‐ordinate relative to ⌜ cannot exceed the corresponding number for ⌜ * .