The Hardy inequality and nonlinear parabolic equations on Carnot groups
Nonlinear Analysis, Theory, Methods and Applications, vol.69, no.12, pp.4643-4653, 2008 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 69 Issue: 12
- Publication Date: 2008
- Doi Number: 10.1016/j.na.2007.11.020
- Journal Name: Nonlinear Analysis, Theory, Methods and Applications
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.4643-4653
- Keywords: Hardy-type inequality, Nonlinear parabolic equations, Positive solutions
- Open Archive Collection: AVESIS Open Access Collection
- İstanbul Ticaret University Affiliated: Yes
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.