Publication at Faculty of Mathematics and Physics |
2020
Abstract
We establish higher integrability up to the boundary for the gradient of solutions to porous medium type systems, whose model case is given by partial derivative(t)u - Delta(vertical bar u vertical bar(m-1)u) = div F, where m > 1. More precisely, we prove that under suitable assumptions the spatial gradient D(vertical bar u vertical bar(m-1)u) of any weak solution is integrable to a larger power than the natural power 2.
Our analysis includes both the case of the lateral boundary and the initial boundary.