An optimal Liouville theorem for the porous medium equation

DOI10.1007/S00013-022-01706-4zbMath1487.35138arXiv2201.02031OpenAlexW4210440692WikidataQ113906377 ScholiaQ113906377MaRDI QIDQ2131245

Damião J. Araújo, Rafayel Teymurazyan

Publication date: 25 April 2022

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2201.02031

zbMATH Keywords

Liouville theoremporous medium equationdegenerate parabolic equationsintrinsic scaling

Mathematics Subject Classification ID

Flows in porous media; filtration; seepage (76S05) Degenerate parabolic equations (35K65) Quasilinear parabolic equations (35K59) Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs (35B53)

Cites Work

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• The obstacle problem for the porous medium equation
• Harnack estimates for quasi-linear degenerate parabolic differential equations
• An optimal Liouville-type theorem for radial entire solutions of the porous medium equation with source
• Elliptic partial differential equations of second order
• Higher regularity estimates for the porous medium equation near the heat equation
• Liouville-type theorems and universal bounds for nonnegative solutions of the porous medium equation with source
• A geometric tangential approach to sharp regularity for degenerate evolution equations
• An intrinsic Liouville theorem for degenerate parabolic equations
• A note on the heat equation
• Hölder Regularity for Singular Parabolic Obstacle Problems of Porous Medium Type

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