References & Citations
Mathematics > Analysis of PDEs
Title: Liouville rigidity and time-extrinsic Harnack estimates for an anisotropic slow diffusion
(Submitted on 7 Nov 2022 (v1), last revised 22 Feb 2023 (this version, v2))
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.
Submission history
From: Simone Ciani [view email][v1] Mon, 7 Nov 2022 08:28:05 GMT (34kb)
[v2] Wed, 22 Feb 2023 17:50:40 GMT (35kb)
Link back to: arXiv, form interface, contact.