Revista Matemática Iberoamericana
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Published online: 2018-05-28
Parabolic Harnack inequality on fractal-type metric measure Dirichlet spacesJanna Lierl (1) University of Connecticut, Storrs, USA
This paper proves the strong parabolic Harnack inequality for local weak solutions to the heat equation associated with time-dependent (nonsymmetric) bilinear forms. The underlying metric measure Dirichlet space is assumed to satisfy the volume doubling condition, the strong Poincaré inequality, and a cutoff Sobolev inequality. The metric is not required to be geodesic. Further results include a weighted Poincaré inequality, as well as upper and lower bounds for non-symmetric heat kernels.
Keywords: Parabolic Harnack inequality, Moser iteration, weighted Poincaré inequality, heat kernel estimates, non-symmetric Dirichlet form, fractals
Lierl Janna: Parabolic Harnack inequality on fractal-type metric measure Dirichlet spaces. Rev. Mat. Iberoam. 34 (2018), 687-738. doi: 10.4171/RMI/1001