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Definition and properties of supersolutions to the porous medium equation
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Juha Kinnunen
Published/Copyright:
July 1, 2008
Abstract
We study a wide class of supersolutions of the porous medium equation. These supersolutions are defined as lower semicontinuous functions obeying the comparison principle. We show that they have a spatial Sobolev gradient and give sharp summability exponents. We also study pointwise behaviour.
Received: 2006-10-30
Revised: 2007-02-07
Published Online: 2008-07-01
Published in Print: 2008-May
© Walter de Gruyter Berlin · New York 2008
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- Definition and properties of supersolutions to the porous medium equation
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Articles in the same Issue
- On the positive extension property and Hilbert's 17th problem for real analytic sets
- Projective integral models of Shimura varieties of Hodge type with compact factors
- Résolutions flasques des groupes linéaires connexes
- Definition and properties of supersolutions to the porous medium equation
- Gevrey series in quantum topology
- Symplectic singularities of varieties: The method of algebraic restrictions
