Local Hopf Lemma for Certain Degenerate Elliptic Operators on the Half-Space

초록

We prove that the local Hopf lemma of Baouendi-Rothschild for harmonic functions continues to hold for the degenerate elliptic operator, L-a = x(a)?(2)(x) + S-j=1(n) ?(2)(y)(j ), on the half-space when the degeneracy exponent a is less than 2. We provide examples of degenerate elliptic operators with the degeneracy exponent greater or equals to 2 for which the local Hopf lemma fail.

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