The Hardy inequality and nonlinear parabolic equations on Carnot groups
Abstract
In this paper we shall investigate the nonexistence of positive solutions for the following nonlinear parabolic partial differential equation: {(frac(∂ u, ∂ t) = ΔG, p u + V (x) up - 1, in Ω × (0, T), 1 < p < 2,; u (x, 0) = u0 (x) ≥ 0, in Ω,; u (x, t) = 0, on ∂ Ω × (0, T),) where ΔG, p is the p-sub-Laplacian on a Carnot group G and V ∈ Lloc1 (Ω). © 2007 Elsevier Ltd. All rights reserved.
Publication Title
Nonlinear Analysis, Theory, Methods and Applications
Recommended Citation
Goldstein, J., & Kombe, I. (2008). The Hardy inequality and nonlinear parabolic equations on Carnot groups. Nonlinear Analysis, Theory, Methods and Applications, 69 (12), 4643-4653. https://doi.org/10.1016/j.na.2007.11.020
COinS
