Remarks on the local Hopf’s lemma
Vladimir Shklover · Proceedings of the American Mathematical Society · 1996
The paper deals with the problem of extending the recent work of M.S.Baouendi and L.P.Rothschild concerning harmonic functions vanishing to infinite order in the normal direction in balls and half-spaces. Contrary to what one expects, we show that the B.-R. result extends neither to arbitrary domains nor to cases when the normal is replaced by a curve transversal to the boundary. The exact criterion when the result holds in R 2 \mathbf {R}^2 is given.