## Differential and Integral Equations

### Local and global boundedness for some nonlinear parabolic equations exhibiting a time singularity

#### 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.

#### Article information

Source
Differential Integral Equations Volume 29, Number 11/12 (2016), 1029-1048.

Dates
First available in Project Euclid: 13 October 2016