We prove some Hardy-type inequalities related to quasilinear second-order degenerate elliptic differential operators L p u := −∇ L (|∇ L u| p−2 ∇ L u). If φ is a positive weight such that −L p φ ≥ 0, then the Hardy-type inequality c |u| p |∇ φ| p dξ ≤ L φp |∇ u| p dξ L 1 u ∈ C 0( ) holds. We find an explicit value of the constant involved, which, in most cases, results optimal. As particular case we derive Hardy inequalities for subelliptic operators on Carnot Groups.

Hardy Type Inequalities Related to Degenerate Elliptic Differential Operators

D'AMBROSIO, Lorenzo
2005-01-01

Abstract

We prove some Hardy-type inequalities related to quasilinear second-order degenerate elliptic differential operators L p u := −∇ L (|∇ L u| p−2 ∇ L u). If φ is a positive weight such that −L p φ ≥ 0, then the Hardy-type inequality c |u| p |∇ φ| p dξ ≤ L φp |∇ u| p dξ L 1 u ∈ C 0( ) holds. We find an explicit value of the constant involved, which, in most cases, results optimal. As particular case we derive Hardy inequalities for subelliptic operators on Carnot Groups.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11586/47756
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