ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 30, 76 Nasyrov, Samyon, Kazan State University, Russia Robin capacity and lift of infinitely thin airfoils In 1934 M. A. Lavrent’ev proved the following result. Let l and K_{0} be positive constants, K_{0}l < 1/21 (∗). Denote Γ the class of all plane arcs γ of length l with the curvature K(s) ≤ K_{0}, s ∈ [0, l] where s is the arc length of γ. Then an arc of a circle of radius K_{0}^{−1} and length l has maximal aerodynamic lift amongst all arcs γ ∈ Γ. Using the notions of Robin capacity and extremal length family of curves we increase more than twice the constant 1/21 in (∗). We also show that the lift of an airfoil is the difference between Robin capacities of the upper and the lower parts of its boundary. Nonconstant majorants for K(s) are considered, too.