Remarks on the local Hopf’s lemma

Shklover, Vladimir

doi:10.1090/S0002-9939-96-03367-9

Remarks on the local Hopf’s lemma
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by Vladimir Shklover

Proc. Amer. Math. Soc. 124 (1996), 2711-2716

DOI: https://doi.org/10.1090/S0002-9939-96-03367-9

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Abstract:

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 $\mathbf {R}^2$ is given.

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