Annales Academię Scientiarum Fennicę
Mathematica
Volumen 37, 2012, 571-577
University of Eastern Finland, Department of Physics and Mathematics
P.O. Box 111, FI-80101 Joensuu, Finland; olli.toivanen 'at' uef.fi
Abstract. We prove Harnack's inequality for general solutions of elliptic equations
-\div A(x,u,\nabla u) = B(x,u,\nabla u),
where A and B satisfy natural structural conditions with respect to a variable growth exponent p(x). The proof is based on a modification of the Caccioppoli inequality, which enables us to use existing versions of the Moser iteration.
2010 Mathematics Subject Classification: Primary 49N60; Secondary 35J60.
Key words: Non-standard growth, variable exponent, Caccioppoli estimate, Moser iteration, weak Harnack inequality.
Reference to this article: O. Toivanen: Harnack's inequality for general solutions with nonstandard growth. Ann. Acad. Sci. Fenn. Math. 37 (2012), 571-577.
doi:10.5186/aasfm.2012.3736
Copyright © 2012 by Academia Scientiarum Fennica