Resumen de Smooth potentials with prescribed boundary behaviour

Stephen J. Gardiner, Anders Gustafsson

• This paper examines when it is possible to find a smooth potential on a C1 domain D with prescribed normal derivatives at the boundary. It is shown that this is always possible when D is a Liapunov-Dini domain, and this restriction on D is essential. An application concerning C1 superharmonic extension is given.