Strong uniqueness for second order differential operators

[摘要] We prove a strong unique continuation result for differential inequalities of the form \P(x,D)u\ less than or equal to C-1 \x\(-2)\u\ + C-2 \x\(-1) \del u\, where P(x,D) = Sigma(j,k=1)(n) a(jk)(x) DjDk is an elliptic second order differential operator with Lipschitz coefficients such that a(jk)(0) is real. C-1 and C-2 are positive constants such that C-2 is sufficiently small. Our assumption on the constant C-2 is justified by counterexamples due to Alinhac and Baouendi [2] and Wolff [6] showing that the strong unique continuation fails if C-2 is not small. (C) 1997 Academic Press.

[发布日期] 1997-12-10