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.
Show me the PDF file (311 KB), TEX file, and other files for this article.
| Josef Danecek |
Institute of Mathematics and Biomathematics, Faculty of Science
University of South Bohemia, Branisovska 31
3705 Ceske Budejovice, Czech Republic
| Eugen Viszus |
Department of Mathematical Analysis and Numerical Mathematics
Faculty of Mathematics, Physics and Informatics
Comenius University, Mlynska dolina
84248 Bratislava, Slovak Republic
Return to the EJDE web page