On the geometric form of Bernoulli configurations

✍ Scribed by Andrew Acker

• Publisher: John Wiley and Sons
• Year: 1988
• Tongue: English
• Weight: 839 KB
• Volume: 10
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.1670100102

✦ Synopsis

In References 4 and 5, the author studied the geometric form of the free boundary r of an annula; domain Q, characterized by the Bernoulli condition that IVU1= 1 on r, where U is the capacity potential in R. It was shown, for example, that has at most as many v-extrema (for a given direction v) or inflection points as the other boundary component r* of Q, 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.