Gradient estimates for the porous medium equation
 
 
Description:  The sharp regularity of weak solutions to the porous medium equation is a long-standing open problem. The fundamental solution of the problem, the so called Barenblatt solution, is known to be C^{1/(m-1)}-Hölder continuous, and it is a natural question whether this is the worst possible behavior. A counter-example by Aronson and Graveleau, however, suggests that this is not the case - leaving the question wide open. Known results by Gilding and Ivanov provide a tight link between the Hölder-regularity and gradient estimates for the solutions. In this talk, I will present some new results concerning the topic. The talk is based on a joint work with Ugo Gianazza.
Date:  2016-04-22
Start Time:   14:30
Speaker:  Juhana Siljander (Univ. Jyväskylä, Finland)
Institution:  University of Jyväskylä, Finland
Place:  Sala 5.5
Research Groups: -Analysis
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