Moring K, Scheven C, Schwarzacher S, Singer T (2020)
Publication Type: Journal article
Publication year: 2020
Book Volume: 19
Pages Range: 1697-1745
Journal Issue: 3
DOI: 10.3934/cpaa.2020069
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.
APA:
Moring, K., Scheven, C., Schwarzacher, S., & Singer, T. (2020). Global higher integrability of weak solutions of porous medium systems. Communications on Pure and Applied Analysis, 19(3), 1697-1745. https://dx.doi.org/10.3934/cpaa.2020069
MLA:
Moring, Kristian, et al. "Global higher integrability of weak solutions of porous medium systems." Communications on Pure and Applied Analysis 19.3 (2020): 1697-1745.
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