Capacity of a condenser whose plates are circular arcs

Details Capacity of a condenser whose plates are circular arcs Capacity of a condenser whose plates are circular arcs

2006-04-03

arxiv.org/abs/math/0604033v1

Complex Variables: Theory and Applications, An International Journal, vol.50, no.2 (2005), 103-122

Mathematics

Complex Variables

15 pages, 1 figure

Scientific paper

We find an asymptotic formula for the conformal capacity of a plane condenser both plate of which are concentric circular arcs as the distance between them vanishes. This result generalizes the formula for the capacity of parallel linear plate condenser found by Simonenko and Chekulaeva in 1972 and sheds light on the problem of finding an asymptotic formula for the capacity of condenser whose plates are arbitrary parallel curves. This problem was posed and partially solved by R. K\"{u}hnau in 1998.

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