Local hardy and rellich inequalities for sums of squares of vector fields

Michael Ruzhansky; Durvudkhan Suragan

Local hardy and rellich inequalities for sums of squares of vector fields

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Abstract

We prove local refined versions of Hardy's and Rellich's inequalities as well as of uncertainty principles for sums of squares of vector fields on bounded sets of smooth manifolds under certain assumptions on the vector fields. We also give some explicit examples, in particular, for sums of squares of vector fields on Euclidean spaces and for sub-Laplacians on stratified Lie groups.

Original language	English
Pages (from-to)	505-540
Number of pages	36
Journal	Advances in Differential Equations
Volume	22
Issue number	7-8
Publication status	Published - Jul 1 2017
Externally published	Yes

ASJC Scopus subject areas

Analysis
Applied Mathematics

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abstract = "We prove local refined versions of Hardy's and Rellich's inequalities as well as of uncertainty principles for sums of squares of vector fields on bounded sets of smooth manifolds under certain assumptions on the vector fields. We also give some explicit examples, in particular, for sums of squares of vector fields on Euclidean spaces and for sub-Laplacians on stratified Lie groups.",

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