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Keywords:
nonlinear elliptic systems; regularity; Campanato-Morrey spaces
Summary:
We provide an explicit example of a nonlinear second order elliptic system of two equations in three dimension to compare two $C^{0,\gamma}$-regularity theories. We show that, for certain range of parameters, the theory developed in {\it Dan\v{e}\v{c}ek, Nonlinear Differential Equations Appl.\/} {\bf 9} (2002), gives a stronger result than the theory introduced in {\it Koshelev, Lecture Notes in Mathematics,} {\bf 1614}, 1995. In addition, there is a range of parameters where the first theory gives H"{o}lder continuity of solution for all $\gamma<1$, while the {\it Koshelev} theory is not applicable at all.
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