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The Porous Medium Equation and Convexity
Abstract
We show that root convexity of the pressure is preserved by the porous medium equation if the initial data is root convex, positive, smooth, bounded below by a quadratic function and has bounded Laplacian. This complements a result of Daskalopoulos-Hamilton-Lee on root concavity of pressure.
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BibTeX
@misc{yu2026porous,
title = {{The Porous Medium Equation and Convexity}},
author = {Ning Yu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30358},
eprint = {2610.30358},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30358},
}
RIS
TY - UNPB
TI - The Porous Medium Equation and Convexity
AU - Ning Yu
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.30358
UR - https://arxiv.org/abs/2610.30358
AB - We show that root convexity of the pressure is preserved by the porous medium equation if the initial data is root convex, positive, smooth, bounded below by a quadratic function and has bounded Laplacian. This complements a result of Daskalopoulos-Hamilton-Lee on root concavity of pressure.
ER -