Parabolic Harnack inequality for time-dependent non-symmetric Dirichlet forms

2012/05/29 by Lierl, Janna, Saloff-Coste, Laurent
#31E05 #35K05 #58J65 #60J60 #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1205.6493

Abstract

In the context of a metric measure Dirichlet space satisfying volume doubling and Poincaré inequality, we prove the parabolic Harnack inequality for weak solutions of the heat equation associated with local nonsymmetric bilinear forms. In particular, we show that these weak solutions are locally bounded.

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