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September/October 2012 Harnack's inequality for parabolic De Giorgi classes in metric spaces
Juha Kinnunen, Niko Marola, Michele Miranda Jr., Fabio Paronetto
Adv. Differential Equations 17(9/10): 801-832 (September/October 2012).

Abstract

In this paper we study problems related to parabolic partial differential equations in metric measure spaces equipped with a doubling measure and supporting a Poincaré inequality. We give a definition of parabolic De Giorgi classes and compare this notion with that of parabolic quasiminimizers. The main result, after proving the local boundedness, is a scale- and location-invariant Harnack inequality for functions belonging to parabolic De Giorgi classes. In particular, the results hold true for parabolic quasiminimizers.

Citation

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Juha Kinnunen. Niko Marola. Michele Miranda Jr.. Fabio Paronetto. "Harnack's inequality for parabolic De Giorgi classes in metric spaces." Adv. Differential Equations 17 (9/10) 801 - 832, September/October 2012.

Information

Published: September/October 2012
First available in Project Euclid: 17 December 2012

zbMATH: 1255.30057
MathSciNet: MR2985675

Subjects:
Primary: 30L99, 31E05, 35K05, 49N60, 5K99

Rights: Copyright © 2012 Khayyam Publishing, Inc.

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Vol.17 • No. 9/10 • September/October 2012
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