On Bounding Harmonic Functions by Linear Interpolation

Abstract

+ (y — y0) 2 = A can be written in the form 1 r « R(0 + v)u(R(d), 6) + R(9 + ir)u(R(d + T), 6 + ir) u(0) = — I dd, 2TTJ o R(6) + R(0 + T) where r = R(6) is the polar equation of the boundary. Thus the value of a harmonic function at any point in a circle is an average of the values obtained by linear interpolation of the boundary values at the ends of each… (More)

Topics

Figures and Tables

Sorry, we couldn't extract any figures or tables for this paper.