The Schwarz reflection principle for harmonic functions in R2 subject to the Robin condition

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:348

Article

Belinskiy, Boris P.²  Savina, Tatiana V.¹ 

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

[2] Univ Tennessee, Chattanooga, TN 37403 USA

关键词: reflection principle;    harmonic functions;    Robin condition;   

DOI  :  10.1016/j.jmaa.2008.08.010

来源: Elsevier

【 摘 要 】

A non-local reflection formula for harmonic functions in R-2 satisfying the Robin boundary condition, alpha partial derivative(n)u + beta u = 0, on a real-analytic curve is suggested. This formula generalizes the celebrated Schwarz reflection principle. It is also shown how the obtained formula reduces to well-known point-to-point reflection laws corresponding the Dirichlet and Neumann boundary conditions when one of the coefficients, alpha or beta, vanishes. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free