English

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.

Keywords

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

R2 v1 2026-06-23T03:14:45.668Z