Gadjiev T. S.
Ukr. Mat. Zh. - 2014. - 66, № 8. - pp. 1041–1057
We establish necessary and sufficient conditions of removability of compact sets.
On removable sets of solutions of second-order elliptic and parabolic equations in nondivergent form
Ukr. Mat. Zh. - 2009. - 61, № 11. - pp. 1485-1496
We consider nondivergent elliptic and parabolic equations of the second order whose leading coefficients satisfy the uniform Lipschitz condition. We find a sufficient condition for the removability of a compact set with respect to these equations in the space of Hölder functions.
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
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.