Geometric second derivative estimates in Carnot groups and convexity
| dc.creator | Garofalo, Nicola | |
| dc.date | 2008-03-07 | |
| dc.date.accessioned | 2026-07-07T09:25:37Z | |
| dc.date.available | 2026-07-07T09:25:37Z | |
| dc.description | We prove some new a priori estimates for H_2-convex functions which are zero on the boundary of a bounded smooth domain Ωin a Carnot group G. Such estimates are global and are geometric in nature as they involve the horizontal mean curvature \mathcal H of the boundary of Ω. As a consequence of our bounds we show that if G has step two, then for any smooth $H_2$-convex function in Ω\subset G vanishing on the boundary of Ωone has \sum_{i,j=1}^m \int_Ω([X_i,X_j]u)^2 dg \leq {4/3} \int_{\partial Ω} \mathcal H |\nabla_H u|^2 dσ_H . | |
| dc.identifier | https://arxiv.org/abs/0803.1021 | |
| dc.identifier | http://arxiv.org/abs/0803.1021 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/156462 | |
| dc.subject | Analysis of PDEs | |
| dc.title | Geometric second derivative estimates in Carnot groups and convexity | |
| dc.type | text |