Morrey Regularity of Solutions of Nonlinear Elliptic Systems of Arbitrary Order with Restrictions on the Modulus of Ellipticity - Kalita, E. A. (Ukrains’kyi Matematychnyi Zhurnal, 2002)
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.