2019
Том 71
№ 11

All Issues

Kalita E. A.

Articles: 8
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 (Russian)

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 (Russian)

On nonlinear higher order elliptic systems positive in the first derivatives

Kalita E. A.

↓ Abstract   |   Full text (.pdf)

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

Elliptic systems of a divergent type with a natural energy space $W^m_p \bigcap W^l_q$ are considered. Under certain restrictions imposed on the modulus of ellipticity of the lower part of the system, the Hölder property of the generalized solutions to this system and the Liouville theorem are established.

Article (Russian)

Properties of the solutions of multilinear elliptical systems of nondivergence type

Kalita E. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1992. - 44, № 2. - pp. 184–191

Results on the existence of finite and infinite singular points are obtained for multilinear elliptical systems that satisfy an analogue of the Cordes condition.

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