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arXiv · 2403.13226

Non-preservation of $\alpha$-concavity for the porous medium equation in higher dimensions

Xi Sisi Shen·Pranay Talla
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Abstract

In this short note, we prove that $\alpha$-concavity of the pressure is not preserved for the porous medium equation in dimensions $n=3$ and higher for any $\alpha\in [0,1]\backslash \{\frac{1}{2}\}$. Together with the result of Chau-Weinkove for $n=2$, this fully resolves an open problem posed by V\'asquez on whether pressure concavity is preserved in general for the porous medium equation.

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Xi Sisi Shen, Pranay Talla. 2024-03-20. Non-preservation of $\alpha$-concavity for the porous medium equation in higher dimensions. https://arxiv.org/abs/2403.13226

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