Moring/Schätzler: Higher integrability for singular doubly nonlinear systems

Date: 2024-05-22

Time: 10:30 - 11:00

Zoom link:

Kristian Moring, University of Duisburg-Essen; Leah Schätzler, University of Salzburg


We present a local higher integrability result for the spatial gradient of weak solutions \(u \colon \Omega_T \to \mathbb{R}^N\) to doubly nonlinear parabolic systems whose prototype is \begin{equation*} \partial_t \left(|u|^{q-1}u \right) -\mathrm{div} \left( |Du|^{p-2} Du \right) = \mathrm{div}\left( |F|^{p-2} F \right) \quad \text{ in } \Omega_T := \Omega \times (0,T) \end{equation*} with parameters \(p>1\) and \(q>0\) and an open set \(\Omega\subset\mathbb{R}^n\). We are concerned with the range \(q>1\), i.e.~the singular case with respect to the porous medium type nonlinearity, and \(p>\frac{n(q+1)}{n+q+1}\). A key ingredient in the proof is an intrinsic geometry that takes both the solution \(u\) and its spatial gradient \(Du\) into account.

The talk is based on joint work with Christoph Scheven.