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On non-homogeneous Robin reflection for harmonic functions.
- Source :
-
Applicable Analysis . Mar2022, Vol. 101 Issue 5, p1699-1714. 16p. - Publication Year :
- 2022
-
Abstract
- This paper concerns the reflection of harmonic functions, w (x , y) , defined in a neighborhood of a real-analytic curve in the plane subject to the Robin condition, a w + b ∂ n w = φ w , on that curve. Here a and b are constants, and φ w is the restriction of a holomorphic function onto the curve. For the case, when φ w = 0 , while a and b are real-analytic functions, a reflection formula was derived in Belinskiy and Savina [The Schwarz reflection principle for harmonic functions in R 2 subject to the Robin condition. J Math Anal Appl. 2008;348:685–691], using the reflected fundamental solution method. Here, we construct a Robin-to-Neumann mapping and use it for obtaining the reflection operator. Since the two formulae look different, we show their equivalence when a and b are constants and φ w = 0. As examples, we show reflection formulae for non-homogeneous Neumann and Robin conditions on the common within mathematical physics curves, such as circles and lines. [ABSTRACT FROM AUTHOR]
- Subjects :
- *PLANE curves
*MATHEMATICAL physics
*HOLOMORPHIC functions
Subjects
Details
- Language :
- English
- ISSN :
- 00036811
- Volume :
- 101
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- Applicable Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 156475740
- Full Text :
- https://doi.org/10.1080/00036811.2021.1994958