**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.**