Electron. J. Diff. Equ., Vol. 2013 (2013), No. 121, pp. 1-17.

Regularity on the interior for the gradient of weak solutions to nonlinear second-order elliptic systems

Josef Danecek, Eugen Viszus

We consider weak solutions to the Dirichlet problem for nonlinear elliptic systems. Under suitable conditions on the coefficients of the systems we obtain everywhere H\"older regularity on the interior for the gradients of weak solutions. Our sufficient condition for the regularity works even though an excess of the gradient of solution is not very small. More precise partial regularity on the interior can be deduced from our main result. The main result is illustrated through examples at the end of this article.

Submitted April 8, 2013. Published May 16, 2013.
Math Subject Classifications: 35J47.
Key Words: Nonlinear elliptic equations; weak solutions; regularity; Campanato spaces.

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Josef Danecek
Institute of Mathematics and Biomathematics, Faculty of Science
University of South Bohemia, Branisovska 31
3705 Ceske Budejovice, Czech Republic
email: josef.danecek@prf.jcu.cz
Eugen Viszus
Department of Mathematical Analysis and Numerical Mathematics
Faculty of Mathematics, Physics and Informatics
Comenius University, Mlynska dolina
84248 Bratislava, Slovak Republic
email: eugen.viszus@fmph.uniba.sk

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