Global higher integrability of weak solutions of porous medium systems - Moring, Kristian; Scheven, Christoph; Schwarzacher, Sebastian; Singer, Thomas (Communications on Pure and Applied Analysis, 2020)
We establish higher integrability up to the boundary for the gradient of solutions to porous medium type systems, whose model case is given by ∂tu − ∆(|u|m−1u) = div F, where m > 1. More precisely, we prove that under suitable assumptions the spatial gradient D(|u|m−1u) 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.
CRIS-Team Scopus Importer:2019-12-10
Keywords: Gradient estimates; Higher integrability; Porous medium type systems