SEMINARIO DE ANÁLISIS Y APLICACIONES

Lunes, 29 de Octubre de 2018
12:00–13:00, Aula Gris 1 (ICMAT)

Hermann Render

University College Dublin

(Ireland)

Extensions of harmonic functions
vanishing on cylindrical surfaces

Resumen:
The Schwarz reflection principle is a beautiful and important result concerning
the extension of a harmonic function h on a domain
  RN through a relatively
open subset E of @
 on which h vanishes. When N  3 and N is odd,
Ebenfelt and Khavinson have shown that a point-to-point reflection law can
only hold when the containing real analytic surface is either a hyperplane or
a sphere. Thus, for other surfaces in higher dimensions, more elaborate arguments
are required to investigate whether such harmonic extension is still possible.
In this talk we survey new results addressing the problem to extend a
harmonic function which vanishes on a cylindrical surface. The talk is based
on joint work with S.J. Gardiner.
ICMAT CSIC-UAM-UC3M-UCM
Departamento de Matemáticas. U.A.M.