Über die Hölderstetigkeit schwacher Lösungen semilinearer elliptischer Systeme mit einseitiger Bedingung

Abstract

This paper deals with the question if bounded weak solutions of elliptic systems

$$(a_{ij} u_{x_i }^l )_{x_j } = f^l (x,\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{u} ,\nabla \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{u} ),l \leqslant l \leqslant m,$$

, are hölder-continuous. If the f¹ have at most quadratical growth in ∇u and a special structure our answer is affirmative; |u| is supposed not to be too large. The proofs are indirect and yield no a-priori estimates.