2 papers
math.AP2025
Relaxation for highly discontinuous, possibly unbounded, integral functionals
Tommaso Bertin, Giulia Treu
We consider the functional \[ F(u)=\int_Ω f(\nabla u)\,dx\qquad u\inÏ+W^{1,1}_0(Ω) \] where is a Lipschitz bounded open set of , is a su…
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-\…