On the geometric form of Bernoulli configurations
Andrew F. Acker · Mathematical Methods in the Applied Sciences · 1988
Abstract In References 4 and 5, the author studied the geometric form of the free boundary Γ of an annular domain Ω, characterized by the Bernoulli condition that |∇ U |=1 on Γ, where U is the capacity potential in Ω. It was shown, for example, that Γ has at most as many ν‐extrema (for a given direction ν) or inflection points as the other boundary component Γ* of Ω, which is assumed given. Our purpose here is to extend the results in References 4 and 5 (wherever possible) to multiply connected regions for which some boundary components are given and others are free boundaries characterized by the Bernoulli condition. We present both positive results and counterexamples.