2019
Том 71
№ 6

All Issues

Kalita E. A.

Articles: 7
Article (Russian)

Morrey Regularity of Solutions of Nonlinear Elliptic Systems of Arbitrary Order with Restrictions on the Modulus of Ellipticity

Kalita E. A.

↓ Abstract

Ukr. Mat. Zh. - 2002. - 54, № 11. - pp. 1452-1466

We investigate the dependence of the regularity of generalized solutions of nonlinear elliptic systems on the modulus of ellipticity and regularity of the right-hand side. We establish Morrey regularity with limit exponent determined by the modulus of ellipticity in the case where the right-hand side belongs to a space with a norm stronger than the Dini function. These conditions are exact for second-order systems, namely, for any violation of the Dini condition, we construct a solution that does not belong to the Morrey space with limit exponent.

Article (Russian)

Solvability of nonlinear elliptic systems with measure

Kalita E. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1996. - 48, № 7. - pp. 925-939

We prove the solvability of nonlinear elliptic systems in spaces dual to the Morrey spaces. As a main consequence, we establish that, under certain restrictions on the modulus of ellipticity of a system, systems with measure are solvable.

Brief Communications (Russian)

Exactness of the cordes condition of the Hölder property for the gradient of nondivergent elliptic systems

Kalita E. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1995. - 47, № 2. - pp. 292–294

We give an example of a nondivergent elliptic system showing that the classical Cordes condition of the Hölder property for the gradient of solution of a nondivergent elliptic equation is exact if properly extended onto systems.

Article (Ukrainian)

Partial regularity of traces of solutions of higher-order nonlinear elliptic systems

Kalita E. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1993. - 45, № 11. - pp. 1495–1502

For traces of generalized solutions of elliptic systems on smooth manifolds, we study the dependence of the Hausdorff dimension of the set of points at which a solution is not smooth on the modulus of ellipticity of a system.

Article (Ukrainian)

On nonlinear higher order elliptic systems positive in the first derivatives

Kalita E. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1993. - 45, № 7. - pp. 942–947

Article (Ukrainian)

Regularity of a boundary point for quasilinear elliptic systems of the second order

Kalita E. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1991. - 43, № 5. - pp. 590–596

Article (Ukrainian)

Liouville theorem for higher-order elliptic systems of cordes type

Kalita E. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1991. - 43, № 2. - pp. 199-205