, Volume 41, Issue 1, pp 35-60

Unique continuation for parabolic operators

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Abstract

It is shown that if a functionu satisfies a backward parabolic inequality in an open set Ω∉R n+1 and vanishes to infinite order at a point (x 0·t 0) in Ω, thenu(x, t 0)=0 for allx in the connected component ofx 0 in Ω⌢(R n ×{t 0}).