ABSTRACT
A domain in the plane is said to have real analytic boundary if its boundary can be (locally) parameterized by a function z(t) = x(t) + iy(t) where the real valued functions x(t) and y(t) are equal to their (real) Taylor series expansions in (t − t0) in a neighborhood of each point t0 in the parameter space. A function v(x, y) will be said to be real analytic on an open set in the plane if it can be expanded in a power series v(x, y) =
∑ anm(x−x0)n(y− y0)m that converges on a neighborhood of
each point (x0, y0) in the open set. Note that harmonic functions are real analytic because they are locally the real part of holomorphic functions.
