The Hardy inequality and nonlinear parabolic equations on Carnot groups

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Goldstein J. A., KÖMBE İ.

Nonlinear Analysis, Theory, Methods and Applications, cilt.69, sa.12, ss.4643-4653, 2008 (SCI-Expanded) identifier

  • 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
  • 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.