The Hardy inequality and nonlinear parabolic equations on Carnot groups
Nonlinear Analysis, Theory, Methods and Applications, cilt.69, sa.12, ss.4643-4653, 2008 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 69 Sayı: 12
- Basım Tarihi: 2008
- Doi Numarası: 10.1016/j.na.2007.11.020
- Dergi Adı: Nonlinear Analysis, Theory, Methods and Applications
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.4643-4653
- Anahtar Kelimeler: Hardy-type inequality, Nonlinear parabolic equations, Positive solutions
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- İstanbul Ticaret Üniversitesi Adresli: Evet
Özet
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.