3 papers
math.AP2025
Parabolic PDEs with Dynamic Data under a Bounded Slope Condition
Verena Bögelein, Frank Duzaar, Giulia Treu
We establish the existence of Lipschitz continuous solutions to the Cauchy Dirichlet problem for a class of evolutionary partial differential equations of the form $$ \partial_tu-\…
math.AP2025
Local boundedness and higher integrability for the sub-critical singular porous medium system
Verena Bögelein, Frank Duzaar, Ugo Gianazza +1
The gradient of weak solutions to porous medium-type equations or systems possesses a higher integrability than the one assumed in the pure notion of a solution. We settle the crit…
math.AP2018
Regularity of weak solutions and supersolutions to the porous medium equation
Verena Bögelein, Pekka Lehtelä, Stefan Sturm
We study the relations between different regularity assumptions in the definition of weak solutions and supersolutions to the porous medium equation. In particular, we establish th…