From reflections to elliptic growth
Complex Variables
2018-07-27 v1 Analysis of PDEs
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.
Cite
@article{arxiv.1807.09903,
title = {From reflections to elliptic growth},
author = {Tatiana Savina},
journal= {arXiv preprint arXiv:1807.09903},
year = {2018}
}
Comments
19 pp