Smooth potentials with prescribed boundary behaviour

Resum

This paper examines when it is possible to find a smooth potential on a $C^{1}$ 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 $C^{1}$ superharmonic extension is given.