Higher integrability for singular doubly nonlinear systems
Higher integrability for singular doubly nonlinear systems
Abstract We prove a local higher integrability result for the spatial gradient of weak solutions to doubly nonlinear parabolic systems whose prototype is $$\begin{aligned} \partial _t \left( |u|^{q-1}u \right) -{{\,\textrm{div}\,}}\left( |Du|^{p-2} Du \right) = {{\,\textrm{div}\,}}\left( |F|^{p-2} F \right) \quad \text { in } \Omega _T:= \Omega \times (0,T) \end{aligned}$$ <mml:math …