Geodesic
Liouville theorems for the solution of a~second-order linear parabolic equation with discontinuous coefficients
Matematičeskie zametki, Tome 5 (1969) no. 5, pp. 599-606.

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Theorems of Liouville type are proved for a very general second-order parabolic equation. Smoothness conditions are not imposed on the coefficients; however, it is required that a Cordes condition be satisfied which denotes the nearness to the identity of the coefficient matrix for the second derivatives. 
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     author = {R. Ya. Glagoleva},
     title = {Liouville theorems for the solution of a~second-order linear parabolic equation with discontinuous coefficients},
     journal = {Matemati\v{c}eskie zametki},
     pages = {599--606},
     publisher = {mathdoc},
     volume = {5},
     number = {5},
     year = {1969},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1969_5_5_a12/}
}
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R. Ya. Glagoleva. Liouville theorems for the solution of a~second-order linear parabolic equation with discontinuous coefficients. Matematičeskie zametki, Tome 5 (1969) no. 5, pp. 599-606. http://geodesic.mathdoc.fr/item/MZM_1969_5_5_a12/