MATHEMATICA BOHEMICA, Vol. 135, No. 2, pp. 199-207, 2010

On Holder regularity for vector-valued
minimizers of quasilinear functionals

Josef Danecek, Eugen Viszus

Josef Danecek, Institute of Mathematics and Biomathematics, Faculty of Science, University of South Bohemia, Branisovska 31, 370 05 Ceske Budejovice, Czech Republic, e-mail: josef.danecek@prf.jcu.cz; Eugen Viszus, Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynska dolina, 842 48 Bratislava, Slovak Republic, e-mail: eugen.viszus@fmph.uniba.sk

Abstract: We discuss the interior Holder everywhere regularity for minimizers of quasilinear functionals of the type
\mathcal{A}(u;\Omega)=\int_{\Omega} A_{ij}^{\alpha\beta}(x,u) D_{\alpha}u^iD_{\beta}u^j\dd x
whose gradients belong to the Morrey space $L^{2,n-2}(\Omega,\mathbb{R}^{nN})$.

Keywords: quasilinear functional, minimizer, regularity, Campanato-Morrey space

Classification (MSC 2010): 35J60

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