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Optimal regularity in
time and space for the porous medium equation
Benjamin Gess, Jonas Sauer and Eitan Tadmor |
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Vol. 13 (2020), No. 8, 2441–2480
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Abstract |
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Regularity estimates in time and space for solutions to the porous medium equation are shown in the scale of Sobolev spaces. In addition, higher spatial regularity for powers of the solutions is obtained. Scaling arguments indicate that these estimates are optimal. In the linear limit, the proven regularity estimates are consistent with the optimal regularity of the linear case. |
Keywords
porous medium equation, entropy solutions, kinetic
formulation, velocity averaging, regularity results
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Mathematical Subject Classification 2010
Primary: 35K59, 35B65, 35D30, 76S05
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Milestones
Received: 19 April 2019
Revised: 30 July 2019
Accepted: 26 September 2019
Published: 28 December 2020
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Authors |
| Benjamin Gess | |
| Max Planck Institute for Mathematics
in the Sciences Leipzig Germany |
Fakultät für Mathematik Universität Bielefeld Bielefeld Germany |
| Jonas Sauer | |
| Max Planck Institute for Mathematics
in the Sciences Leipzig Germany |
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| Eitan Tadmor | |
| Department of Mathematics, Institute
for Physical Science and Technology University of Maryland College Park, MD United States |
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