28 citations · 43 across the 14 of their papers we have counts for
4 papers · 1 filter
Higher integrability for singular doubly nonlinear systems
Kristian Moring, Leah Schätzler, Christoph Scheven
We prove a local higher integrability result for the spatial gradient of weak solutions to doubly nonlinear parabolic systems whose prototype is $$ \partial_t \left(|u|^{q-1}u \rig…
Supercaloric functions for the porous medium equation in the fast diffusion case
Kristian Moring, Christoph Scheven
We study a generalized class of supersolutions, so-called supercaloric functions to the porous medium equation in the fast diffusion case. Supercaloric functions are defined as low…
On two notions of solutions to the obstacle problem for the singular porous medium equation
Kristian Moring, Christoph Scheven
We show that two different notions of solutions to the obstacle problem for the porous medium equation, a potential theoretic notion and a notion based on a variational inequality,…
Hölder Continuity of the Gradient of Solutions to Doubly Non-Linear Parabolic Equations
Verena Bögelein, Frank Duzaar, Ugo Gianazza +2
This paper is devoted to studying the local behavior of non-negative weak solutions to the doubly non-linear parabolic equation \begin{equation*} \partial_t u^q - \text{div}\big(|D…