Remarks on the local Hopf’s lemma
Remarks on the local Hopf’s lemma
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DOI：
10.1090/s0002-9939-96-03367-9
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发表时间：
1996
影响因子：
1.9
通讯作者：
V. Shklover
中科院分区：
文献类型：
--
作者：
V. Shklover
本文讨论了推广M.S.Baouendi和L.P.Rothschild关于球和半空间在法向无穷阶调和函数的最新工作的问题。与人们的预期相反，我们证明了b - r。结果既不扩展到任意域，也不扩展到法线被与边界相交的曲线所取代的情况。给出了结果在R2中成立的确切准则。
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 R2 is given.