A unique continuation theorem for second order parabolic differential operators

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The purpose of this paper is to show that the unique continuation results in [10] extend naturally to the setting of second order parabolic operators. Previously, we showed that if P(x, D) is a second order elliptic differential operator with a C ∞ real principal part, and if |P(x, D)u|≤|Vu| for some V∈L loc n/2 (R n ), then u must vanish identically if it vanishes in an open subset