کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
840833 | 908492 | 2012 | 12 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: A note on Keller–Osserman conditions on Carnot groups A note on Keller–Osserman conditions on Carnot groups](/preview/png/840833.png)
This paper deals with the study of differential inequalities with gradient terms on Carnot groups. We are mainly focused on inequalities of the form Δφu≥f(u)l(|∇0u|)Δφu≥f(u)l(|∇0u|), where ff, ll and φφ are continuous functions satisfying suitable monotonicity assumptions and ΔφΔφ is the φφ-Laplace operator, a natural generalization of the pp-Laplace operator which has recently been studied in the context of Carnot groups. We extend to general Carnot groups the results proved in Magliaro et al. (2011) [7] for the Heisenberg group, showing the validity of Liouville-type theorems under a suitable Keller–Osserman condition. In doing so, we also prove a maximum principle for inequality Δφu≥f(u)l(|∇0u|)Δφu≥f(u)l(|∇0u|). Finally, we show sharpness of our results for a general φφ-Laplacian.
Journal: Nonlinear Analysis: Theory, Methods & Applications - Volume 75, Issue 4, March 2012, Pages 2326–2337