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arXiv · 2211.03357

Liouville rigidity and time-extrinsic Harnack estimates for an anisotropic slow diffusion

Simone Ciani·Umberto Guarnotta
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Abstract

We prove that ancient non-negative solutions to a fully anisotropic prototype evolution equation are constant if they satisfy a condition of finite speed of propagation and if they are both one-sided bounded, and bounded in space at a single time level. A similar statement is valid when the bound is given at a single space point. As a general paradigm, H\"older estimates provide the basics for rigidity. Finally, we show that recent intrinsic Harnack estimates can be improved to a Harnack inequality valid for non-intrinsic times. Locally, they are equivalent.

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Simone Ciani, Umberto Guarnotta. 2022-11-07. Liouville rigidity and time-extrinsic Harnack estimates for an anisotropic slow diffusion. https://arxiv.org/abs/2211.03357

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