Parabolic Variational Problems and Regularity in Metric Spaces
نویسنده
چکیده
In this paper we study variational problems related to the heat equation in metric 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 the proof of a scale-invariant Harnack inequality for functions in parabolic De Giorgi classes. MSC: 30L99, 31E05, 35K05, 35K99, 49N60
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