Abstract for the talk on 14.07.2020 (15:15 h)Oberseminar ANALYSIS - PROBABILITY
Sebastian Schwarzacher (Universität Bonn und Charles Universität Prag)
Higher integrability estimates for parabolic PDEs with fast or slow diffusion
In the talk we discuss some recent results on self-improving properties for gradients of solutions for parabolic evolutions with fast or slow diffusion. The model case is the porous medium equation. We show how local higher integrability estimates can be derived via the celebrated Gehring lemma. The estimates relay on a Calderon Zygmund theory that is developed with respect to an intrinsic metric that depends on the solution; taking into account the local speed of the diffusion. The concept turns out to be flexible enough to show self-improving properties for large classes of diffusions depending on the solution and the gradient.
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