Geodesic
An example of a nonlinear second order elliptic system in three dimension
Commentationes Mathematicae Universitatis Carolinae, Tome 45 (2004) no. 3, pp. 431-442.

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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 $\gamma1$, while the {\it Koshelev} theory is not applicable at all.
Classification : 35B65, 35D10, 35J45, 35J60
Keywords: nonlinear elliptic systems; regularity; Campanato-Morrey spaces 
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Daněček, Josef; Nikodým, Marek. An example of a nonlinear second order elliptic system in three dimension. Commentationes Mathematicae Universitatis Carolinae, Tome 45 (2004) no. 3, pp. 431-442. http://geodesic.mathdoc.fr/item/CMUC_2004__45_3_a4/