A Liouville comparison principle for entire sub- and super-solutions of the equation $u_t-Δ_p (u) = |u|^{q-1}u$

Details A Liouville comparison principle for entire sub- and super-solutions of the equation $u_t-Δ_p (u) = |u|^{q-1}u$ A Liouville comparison principle for entire sub- and super-solutions of the equation $u_t-Δ_p (u) = |u|^{q-1}u$

2011-05-09

arxiv.org/abs/1105.1810v1

Mathematics

Analysis of PDEs

Scientific paper

We establish a Liouville comparison principle for entire sub- and super-solutions of the equation $(\ast)$ $w_t-\Delta_p (w) = |w|^{q-1}w$ in the half-space ${\mathbb S}= {\mathbb R}^1_+\times {\mathbb R}^n$, where $n\geq 1$, $q>0$ and $ \Delta_p (w):={div}_x(|\nabla_x w|^{p-2}\nabla_x w)$, $1

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