Journal Home Page

Cumulative Index

List of all Volumes

Complete Contents
of this Volume

Previous Article

Next Article

Journal of Convex Analysis 28 (2021), No. 1, 179--196
Copyright Heldermann Verlag 2021

Interior Regularity for a Class of Nonlinear Second-Order Elliptic Systems

Josef Danecek
VSB - Technical University of Ostrava, FEECS, Department of Applied Mathematics, 70833 Ostrava-Poruba, Czech Republic

Jana Stará
Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, 18600 Praha 8, Czech Republic

Eugen Viszus
Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University, 84248 Bratislava, Slovak Republic

The interior C1,γ-regularity is proved for weak solutions to a class of nonlinear second-order 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.

[ Fulltext-pdf  (172  KB)] for subscribers only.