Parabolic Harnack inequality for time-dependent non-symmetric Dirichlet   forms
  In the context of a metric measure Dirichlet space satisfying volume doubling and Poincar\'e 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. 
Janna Lierl and Laurent Saloff-Coste
math.PR math.AP