TY - JOUR
T1 - Global higher integrability of weak solutions of porous medium systems
AU - Moring, Kristian
AU - Scheven, Christoph
AU - Schwarzacher, Sebastian
AU - Singer, Thomas
PY - 2020/3
Y1 - 2020/3
N2 - 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.
AB - 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.
KW - Gradient estimates
KW - Higher integrability
KW - Porous medium type systems
UR - http://www.scopus.com/inward/record.url?scp=85075627260&partnerID=8YFLogxK
U2 - 10.3934/cpaa.2020069
DO - 10.3934/cpaa.2020069
M3 - Article
AN - SCOPUS:85075627260
VL - 19
SP - 1697
EP - 1745
JO - COMMUNICATIONS ON PURE AND APPLIED ANALYSIS
JF - COMMUNICATIONS ON PURE AND APPLIED ANALYSIS
SN - 1534-0392
IS - 3
ER -