The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Revista Matemática Iberoamericana


Full-Text PDF (604 KB) | Metadata | Table of Contents | RMI summary
Online access to the full text of Revista Matemática Iberoamericana is restricted to the subscribers of the journal, who are encouraged to communicate their IP-address(es) to their agent or directly to the publisher at
subscriptions@ems-ph.org
Volume 34, Issue 2, 2018, pp. 687–738
DOI: 10.4171/RMI/1001

Published online: 2018-05-28

Parabolic Harnack inequality on fractal-type metric measure Dirichlet spaces

Janna Lierl[1]

(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