Josef Danecek, Eugen Viszus
Abstract:
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 |
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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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