Remark on the strong unique continuation property for parabolic operators

Alessandrini, Giovanni; Vessella, Sergio

doi:10.1090/S0002-9939-03-07142-9

Remark on the strong unique continuation property for parabolic operators
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by Giovanni Alessandrini and Sergio Vessella PDF

Proc. Amer. Math. Soc. 132 (2004), 499-501 Request permission

Abstract:

We consider solutions $u = u(x,t)$, in a neighbourhood of $(x,t) =(0,0)$, to a parabolic differential equation with variable coefficients depending on space and time variables. We assume that the coefficients in the principal part are Lipschitz continuous and that those in the lower order terms are bounded. We prove that, if $u( \cdot ,0)$ vanishes of infinite order at $x=0$, then $u( \cdot ,0) \equiv 0$.

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