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On the geometric form of free boundaries satisfying a bernoulli condition. II
Author(s) -
Acker A.,
Payne L. E.
Publication year - 1986
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.1670080126
Subject(s) - mathematics , boundary (topology) , bernoulli's principle , inflection point , maxima and minima , domain (mathematical analysis) , plane (geometry) , mathematical analysis , jordan curve theorem , geometry , boundary value problem , free boundary problem , pure mathematics , physics , thermodynamics
In the x ‐ y plane, let Ω be an annular domain whose interior boundary Γ* is a known Jordan curve and whose exterior boundary Γ is a free boundary characterized by the condition that|Δ U | = 1 on Γ, where U is the capacity potential in Ω. We obtain a qualitative description of Γ involving such things as its inflection points and local maxima and minima relative to specified directions. We also extend these results to obtain qualitative properties of the free boundary when it is subjected to various geometric contraints. Our results generalize those in [1].