2017
Том 69
№ 9

All Issues

On the smoothness of a solution of the first boundary-value problem for second-order degenerate elliptic-parabolic equations

Gadjiev T. S., Gasimova E. R.

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Abstract

In this work, the first boundary-value problem is considered for second-order degenerate elliptic-parabolic equation with, generally speaking, discontinuous coefficients. The matrix of senior coefficients satisfies the parabolic Cordes condition with respect to space variables. We prove that the generalized solution to the problem belongs to the Holder space C 1+λ if the right-hand side f belongs to Lp, p > n.

English version (Springer): Ukrainian Mathematical Journal 60 (2008), no. 6, pp 831-847.

Citation Example: 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. Mat. Zh. - 2008. - 60, № 6. - pp. 723–736.

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