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On the geometric form of free boundaries satisfying a bernoulli condition
Author(s) -
Acker A.,
Payne L. E.
Publication year - 1984
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670060127
Subject(s) - mathematics , maxima and minima , bernoulli's principle , bounded function , plane (geometry) , maxima , domain (mathematical analysis) , simple (philosophy) , mathematical analysis , jordan curve theorem , geometry , combinatorics , pure mathematics , art , philosophy , epistemology , performance art , engineering , art history , aerospace engineering
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 ⌜ * .
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