Backward uniqueness for the heat equation
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چکیده
According to Gurarii and Matsaev [5], these properties are equivalent, but no proof was ever published. Here is a summary of known results. When n = 1, both properties hold if and only if D is a bounded interval. For PII this is evident, for PI this follows from the results of Tychonov [7]. When n = 2, and D is an angular sector {z : | arg z| < α}, the property PII holds if and only if α < 45◦. Recently, Escauriaza showed that for such sectors PI also holds. He actually proved that PII implies PI for cones. If v is a harmonic function in a cone satisfying PII, then
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