We consider the first boundary-value problem for a second-order degenerate elliptic-parabolic equation with, generally speaking, discontinuous coefficients. The matrix of leading coefficients satisfies the parabolic Cordes condition with respect to space variables. We prove that the generalized solution of the problem belongs to the Hölder space {ie831-01} if the right-hand side f belongs to L p , p > n.
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Published in Ukrains'kyi Matematychnyi Zhurnal, Vol. 60, No. 6, pp. 723–736, June, 2008.
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Gadjiev, T.S., Gasimova, E.R. On the smoothness of a solution of the first boundary-value problem for second-order degenerate elliptic-parabolic equations. Ukr Math J 60, 831–847 (2008). https://doi.org/10.1007/s11253-008-0095-7
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DOI: https://doi.org/10.1007/s11253-008-0095-7