Parabolic variational problems and regularity in metric spaces

Details Parabolic variational problems and regularity in metric spaces Parabolic variational problems and regularity in metric spaces

2011-06-27

arxiv.org/abs/1106.5356v1

Mathematics

Analysis of PDEs

Scientific paper

In this paper we study variational problems related to the heat equation in metric 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 the proof of a scale-invariant Harnack inequality for functions in parabolic De Giorgi classes.

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