A Liouville comparison principle for sub- and super-solutions of the equation w_t-Δ_p (w) = |w|^q-1w

2012/07/10 by Kurta, Vasilii V.
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1207.2496

Abstract

We establish a Liouville comparison principle for entire weak sub- and super-solutions of the equation (∗) w_t-Δ_p (w) = |w|^q-1w in the half-space \mathbb S= \mathbb R¹₊× \mathbb Rⁿ, where n≥ 1, q>0 and Δ_p (w):=div_x(|∇_x w|^p-2∇_x w), 1

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