5 papers
Boundary regularity for parabolic systems in convex domains
Verena Bögelein, Frank Duzaar, Naian Liao +1
In a cylindrical space-time domain with a convex, spatial base, we establish a local Lipschitz estimate for weak solutions to parabolic systems with Uhlenbeck structure up to the l…
On the definition of solution to the total variation flow
Juha Kinnunen, Christoph Scheven
We show that the notions of weak solution to the total variation flow based on the Anzellotti pairing and the variational inequality coincide under some restrictions on the boundar…
Higher integrability in the obstacle problem for the fast diffusion equation
Yumi Cho, Christoph Scheven
We prove local higher integrability of the spatial gradient for solutions to obstacle problems of porous medium type in the fast diffusion case . The result holds for the natu…
Blow-up analysis and boundary regularity for variationally biharmonic maps
Serdar Altuntas, Christoph Scheven
We consider critical points of the bi-energy \[ \int_Ω|Δu|^2\,d x, \] where is a bounded smooth domain of dimension and $N\subset\mathbb{…
Global higher integrability of weak solutions of porous medium systems
Kristian Moring, Christoph Scheven, Sebastian Schwarzacher +1
We establish higher integrability up to the boundary for the gradient of solutions to porous medium type systems, whose model case is given by \begin{equation*} \partial_t u-Δ(|u|^…