Parabolic Harnack inequality on fractal-type metric measure Dirichlet\n spaces

2015/09/15 by Janna Lierl, Lierl, Janna · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.1509.04804

openalex publication_date 2015/09/15 · openalex created_date 2022/09/22 · openalex updated_date 2026/07/28

Abstract

This paper proves the strong parabolic Harnack inequality for local weak\nsolutions to the heat equation associated with time-dependent (nonsymmetric)\nbilinear forms. The underlying metric measure Dirichlet space is assumed to\nsatisfy the volume doubling condition, the strong Poincar 'e inequality, and a\ncutoff Sobolev inequality. The metric is not required to be geodesic. Further\nresults include a weighted Poincar 'e inequality, as well as upper and lower\nbounds for non-symmetric heat kernels.\n

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