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

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