Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 39, 2014, 711-719

ENERGY ESTIMATES FOR VARIATIONAL MINIMIZERS OF A PARABOLIC DOUBLY NONLINEAR EQUATION ON METRIC MEASURE SPACES

Per-Anders Ivert, Niko Marola and Mathias Masson

pa.ivert 'at' gmail.com

University of Helsinki, Department of Mathematics and Statistics
P.O. Box 68, FI-00014 University of Helsinki, Finland; niko.marola 'at' helsinki.fi

Aalto University, School of Science and Technology, Department of Mathematics
P.O. Box 11100, FI-00076 Aalto, Finland; mathias.masson.finland 'at' gmail.com

Abstract. In this paper a variational approach is taken to study a doubly nonlinear parabolic equation. We consider energy estimates for parabolic minimizers related to this equation. These energy estimates play a fundamental role in obtaining Harnack estimates. Our treatment is done in general metric measure spaces with a doubling measure and a Poincaré inequality.

2010 Mathematics Subject Classification: Primary 35B45; Secondary 35K55, 30L99.

Key words: Doubling measure, energy estimates, Harnack inequality, parabolic minimizer, Poincaré inequality, subminimizer, superminimizer.

Reference to this article: P.-A. Ivert, N. Marola and M. Masson: Energy estimates for variational minimizers of a parabolic doubly nonlinear equation on metric measure spaces. Ann. Acad. Sci. Fenn. Math. 39 (2014), 711-719.

Full document as PDF file

doi:10.5186/aasfm.2014.3936