From reflections to elliptic growth

Abstract

We use reflections involving analytic Dirichlet and Neumann data on a real-analytic curve in order to find a representation of solutions to Cauchy problems for harmonic functions in the plane. We apply this representation for finding solutions to Hele-Shaw problems. We also generalize the results by deriving the corresponding formulae for Helmholtz equation and applying them to elliptic growth.

19 pp