Degenerate p-Laplacian operators on H-type groups and applications to Hardy type inequalities
| dc.creator | Jin, Yongyang | |
| dc.creator | Zhang, Genkai | |
| dc.date | 2008-10-29 | |
| dc.date.accessioned | 2026-07-07T10:13:53Z | |
| dc.date.available | 2026-07-07T10:13:53Z | |
| dc.description | Let $\mathbb G$ be a step-two nilpotent group of H-type with Lie algebra $\mathfrak G=V\oplus \mathfrak t$. We define a class of vector fields $X=\{X_j\}$ on $\mathbb G$ depending on a real parameter $k\ge 1$, and we consider the corresponding $p$-Laplacian operator $L_{p,k} u= \text{div}_X (|\na_{X} u|^{p-2} \na_X u)$. For $k=1$ the vector fields $X=\{X_j\}$ are the left invariant vector fields corresponding to an orthonormal basis of $V$, for $k=2$ and $\mathbb G$ being the Heisenberg group they are introduced by Greiner \cite{Greiner-cjm79}. In this paper we obtain the fundamental solution for the operator $L_{p,k}$ and as an application, we get a Hardy type inequality associated with $X$. | |
| dc.description | Canadian Math. J., to appear | |
| dc.identifier | https://arxiv.org/abs/0810.5259 | |
| dc.identifier | http://arxiv.org/abs/0810.5259 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/172692 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Classical Analysis and ODEs | |
| dc.title | Degenerate p-Laplacian operators on H-type groups and applications to Hardy type inequalities | |
| dc.type | text |