The questions of statements in Hölder spaces are studied in the case of inverse problems with boundary conditions of the third kind for general linear and quasilinear parabolic operators with unknown coefficients at the lowest terms. Some sufficient uniqueness conditions for the solutions are derived by using the duality principle. Such an approach allows one to consider the given coefficients of parabolic equations depending not only on the variable x but also on (x,t) in the linear case and on (x,t,u) in the quasilinear case.

Keywords: Hölder spaces, inverse problems, parabolic equations, boundary value problems, duality principle

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