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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…