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Global gradient estimates of porous medium equations under the Finsler-geometric flow

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Abstract

In this paper, we consider a compact n-dimensional Finsler manifold \((M^{n},F(t),m)\) evolving under the Finsler-geometric flow and prove global gradient estimates for positive solutions of porous medium equations \(\partial _{t}u=\Delta _{m}u^{p}\) on \(M^{n}\) where \(\Delta _{m}\) is the Finsler-Laplacian. As applications, by integrating the gradient estimates, we derive Harnack type inequalities. Our results are natural extensions of similar results on Riemannian manifolds under the Riemannian-geometric flow.

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Authors and Affiliations

  1. Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran

    Shahroud Azami

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Azami, S. Global gradient estimates of porous medium equations under the Finsler-geometric flow. Period Math Hung 87, 351–365 (2023). https://doi.org/10.1007/s10998-023-00521-w

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