Parabolic Harnack inequality on fractal-type metric measure Dirichlet spaces

Janna Lierl

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arXiv · 1509.04804

Parabolic Harnack inequality on fractal-type metric measure Dirichlet spaces

Janna Lierl

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Abstract

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 Poincar\'e inequality, and a cutoff Sobolev inequality. The metric is not required to be geodesic. Further results include a weighted Poincar\'e inequality, as well as upper and lower bounds for non-symmetric heat kernels.

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Janna Lierl. 2015-09-16. Parabolic Harnack inequality on fractal-type metric measure Dirichlet spaces. https://arxiv.org/abs/1509.04804

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