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arXiv · 1106.5356

Harnack's Inequality for Parabolic De Giorgi Classes in Metric Spaces

J. Kinnunen·N. Marola·M. Miranda jr.·F. Paronetto
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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 Poincare' 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.

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J. Kinnunen, N. Marola, M. Miranda jr., F. Paronetto. 2013-08-13. Harnack's Inequality for Parabolic De Giorgi Classes in Metric Spaces. https://arxiv.org/abs/1106.5356

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