Work

Harmonic extension through cylindrical and conical surfaces

Year: 2024

Type: article

Abstract: This article describes recent progress concerning the extension of harmonic functions which vanish on a cylindrical or conical surface. The results, which are based on detailed analyses of various expansions of Green functions, can be viewed as partial generalizations of the well-known Schwarz reflection principle to surfaces other than hyperplanes and spheres. Some unexpected features emerge which suggest avenues for further exploration.

Source: Expositiones Mathematicae

DOI: 10.1016/j.exmath.2024.125622

Authors: Stephen J. Gardiner, Hermann Render

Institution: University College Dublin

Language: English

Topic: Analytic and geometric function theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,310

OpenAlex ID: W4403518183

FWCI:

Cites: 16

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Related to: 10