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
Ukr. Mat. Zh. - 1991. - 43, № 5. - pp. 590–596
Ukr. Mat. Zh. - 1991. - 43, № 2. - pp. 199-205