Kalita E. A.
Morrey Regularity of Solutions of Nonlinear Elliptic Systems of Arbitrary Order with Restrictions on the Modulus of Ellipticity
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.
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.
Exactness of the cordes condition of the Hölder property for the gradient of nondivergent elliptic systems
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.
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.
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.
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.
Ukr. Mat. Zh. - 1991. - 43, № 5. - pp. 590–596
Ukr. Mat. Zh. - 1991. - 43, № 2. - pp. 199-205