From reflections to a uniform elliptic growth

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:477

Article

Savina, Tatiana V.¹ 

[1] Ohio Univ, Dept Math, 321 Morton Hall, Athens, OH 45701 USA

关键词: Helc-Shaw problem;    Reflection principle;    Elliptic growth;   

DOI  :  10.1016/j.jmaa.2019.05.021

来源: Elsevier

【 摘 要 】

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 the Helmholtz equation and applying them to a uniform elliptic growth. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free