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Title: An example of a nonlinear second order elliptic system in three dimension (English)
Author: Daněček, Josef
Author: Nikodým, Marek
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 45
Issue: 3
Year: 2004
Pages: 431-442
Category: math
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. (English)
Keyword: nonlinear elliptic systems
Keyword: regularity
Keyword: Campanato-Morrey spaces
MSC: 35B65
MSC: 35D10
MSC: 35J45
MSC: 35J60
idZBL: Zbl 1105.35035
idMR: MR2103138
Date available: 2009-05-05T16:46:20Z
Last updated: 2012-04-30
Stable URL:
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