Advances in Differential Equations
- Adv. Differential Equations
- Volume 17, Number 9/10 (2012), 801-832.
Harnack's inequality for parabolic De Giorgi classes in metric spaces
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.
Adv. Differential Equations, Volume 17, Number 9/10 (2012), 801-832.
First available in Project Euclid: 17 December 2012
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Kinnunen, Juha; Marola, Niko; Miranda Jr., Michele; Paronetto, Fabio. Harnack's inequality for parabolic De Giorgi classes in metric spaces. Adv. Differential Equations 17 (2012), no. 9/10, 801--832. https://projecteuclid.org/euclid.ade/1355702923