Smooth potentials with prescribed boundary behaviour

S. J. Gardiner, A. Gustafsson
2004 Publicacions matemàtiques  
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. 2000 Mathematics Subject Classification. 31B15.
doi:10.5565/publmat_48104_11 fatcat:2l2ymoflb5az7pgyyt2ktb2v4m