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

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 L_p, p > n.