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تسجيل مستخدم جديدParabolic Harnack inequality on fractal-type metric measure Dirichlet spaces
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Janna Lierl
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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 Poincare inequality, and a cutoff Sobolev inequality. The metric is not required to be geodesic. Further results include a weighted Poincare inequality, as well as upper and lower bounds for non-symmetric heat kernels.
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