Title
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
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