Revistes Catalanes amb Accés Obert (RACO)

Smooth potentials with prescribed boundary behaviour

S. J. Gardiner, A. Gustafsson

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.

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