Abstract
Results on the local and global boundedness of nonnegative weak subsolutions of the doubly nonlinear parabolic equation $$ (u^{q})_t-\text{div}\,{(|\nabla u|^{p-2}\nabla u)}=0, $$ are obtained for $p > 1$ and $0 < q < 1$, that is, for equations presenting a singularity in the time derivative part (as well as a singularity, $1 < p < 2$, or degeneracy, $p > 2$, in the principal part of the operator). We work in measure spaces equipped with a doubling non-trivial Borel measure supporting a Poincaré inequality.
Citation
Eurica Henriques. Rojbin Laleoglu. "Local and global boundedness for some nonlinear parabolic equations exhibiting a time singularity." Differential Integral Equations 29 (11/12) 1029 - 1048, November/December 2016. https://doi.org/10.57262/die/1476369328
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