
Journal of Convex Analysis 28 (2021), No. 1, 179196 Copyright Heldermann Verlag 2021 Interior Regularity for a Class of Nonlinear SecondOrder Elliptic Systems Josef Danecek VSB  Technical University of Ostrava, FEECS, Department of Applied Mathematics, 70833 OstravaPoruba, Czech Republic danecek.j@seznam.cz Jana Stará Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, 18600 Praha 8, Czech Republic stara@karlin.mff.cuni.cz Eugen Viszus Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University, 84248 Bratislava, Slovak Republic eugen.viszus@fmph.uniba.sk The interior C^{1,γ}regularity is proved for weak solutions to a class of nonlinear secondorder elliptic systems. It is typical for the system belonging to the class that the continuity moduli of the gradients of its coefficients become slow growing sufficiently far from zero. This property guarantees the regularity of the gradients of solutions to such system in a case when the ellipticity constant is big enough. Some characteristic features of the obtained result are illustrated by examples at the end of the paper. Keywords: Nonlinear elliptic systems, weak solutions, regularity, Campanato spaces. MSC: 35J47. [ Fulltextpdf (172 KB)] for subscribers only. 