Abstract

The interior C1,γC^{1,\gamma}-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.

Author information

Contact details are reproduced from the original publication and may be historical.

Josef Daněček

VŠB - Technical University of Ostrava, FEECS, Department of Applied Mathematics, 70833 Ostrava-Poruba, 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

Keywords

  • Nonlinear elliptic systems
  • weak solutions
  • regularity
  • Campanato spaces

Mathematics Subject Classification

35J47

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Suggested citation

J. Daněček, J. Stará, E. Viszus. “Interior Regularity for a Class of Nonlinear Second-Order Elliptic Systems.” Journal of Convex Analysis 28 (2021), No. 1, 179–196. https://doi.org/10.68381/jca28013

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Published by Heldermann Verlag, 2021. Rights now held by Banach Press.