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Everywhere C-alpha-estimates for a class of nonlinear elliptic systems with critical growth

Publication at Faculty of Mathematics and Physics |
2014

Abstract

We obtain everywhere C-alpha-regularity for vector solutions to a class of nonlinear elliptic systems whose principal part is the Euler operator to a variational integral with quadratic growth in gradient of the unknown and which satisfies a generalized splitting condition and the one-sided condition. If the leading operator is not necessarily elliptic but coercive, possible minima are everywhere Holder continuous and the same holds also for Noether solutions, i.e., extremals which are also stationary with respect to inner variations.The technique of our proof (using weighted norms and inhomogeneous hole-filling method) does not rely on L-infinity-a priori estimates for the solution.