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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_ fatcat:wtxllpwpp5gz7ivfldvahbrkau