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Backward uniqueness for parabolic operators with non-Lipschitz coefficients. (English) Zbl 1334.35074

In the present paper, the uniqueness property for the backward parabolic operator is investigated. The main result indicates some sufficient conditions assuring the uniqueness property. Involved are moduli of continuity, the Osgood condition and assumptions on the coefficients of the operator. Some basics are introduced first: modulus of continuity, the Osgood condition, results of the Littlewood-Paley theory, and Bony’s paraproduct. Furthermore, starting from a modulus of continuity, a weight function is constructed and a Carleman estimate is proved. The uniqueness result is a consequence of this estimate.

MSC:

35K15 Initial value problems for second-order parabolic equations
35R25 Ill-posed problems for PDEs
35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
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References:

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