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Josef Danˇeˇcek, Marek Nikod´ym ) AN=FA B = EA=H IA?@ H@AH AEFJE? IOIJA E JDHAA @EAIE

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Josef Danˇ eˇ cek, Marek Nikod´ ym

An example of a nonlinear second order elliptic system in three dimension

Comment.Math.Univ.Carolinae 45,3 (2004) 431-442.

Abstract: We provide an explicit example of a nonlinear second order elliptic sys- tem of two equations in three dimension to compare twoC0,γ-regularity theories.

We show that, for certain range of parameters, the theory developed in Danˇeˇcek, Nonlinear Differential Equations Appl. 9 (2002), gives a stronger result than the theory introduced in Koshelev, Lecture Notes in Mathematics, 1614, 1995. In ad- dition, there is a range of parameters where the first theory gives H¨older continuity of solution for allγ <1, while the Koshelev theory is not applicable at all.

Keywords: nonlinear elliptic systems, regularity, Campanato-Morrey spaces AMS Subject Classification: 35J60

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