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Degenerate $p$-Laplacian Operators and Hardy Type Inequalities on H-Type Groups

Yongyang Jin ; Genkai Zhang (Institutionen för matematiska vetenskaper, matematik)
Canadian Journal of Mathematics (0008-414X). Vol. 62 (2010), p. 1116-1130.
[Artikel, refereegranskad vetenskaplig]

Let G  be a step-two nilpotent group of H-type with Lie algebra G=V⊕t  . We define a class of vector fields X={X j }  on G  depending on a real parameter k≥1  , and we consider the corresponding p  -Laplacian operator L p,k u=div X (|∇ X u| p−2 ∇ 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 G  being the Heisenberg group the vector fields are the Greiner fields. 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  .

Denna post skapades 2010-02-23. Senast ändrad 2015-12-17.
CPL Pubid: 114090


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