Advances in Differential Equations

Local Hardy and Rellich inequalities for sums of squares of vector fields

Michael Ruzhansky and Durvudkhan Suragan

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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.

Note

The authors were supported in parts by the EPSRC grant EP/K039407/1 and by the Leverhulme Grant RPG-2014-02, as well as by the MESRK grant 5127/GF4. No new data was collected or generated during the course of the research.

Article information

Source
Adv. Differential Equations Volume 22, Number 7/8 (2017), 505-540.

Dates
Accepted: November 2016
First available in Project Euclid: 4 May 2017

Permanent link to this document
https://projecteuclid.org/euclid.ade/1493863420

Zentralblatt MATH identifier
1373.35016

Subjects
Primary: 35A23: Inequalities involving derivatives and differential and integral operators, inequalities for integrals 35H20: Subelliptic equations

Citation

Ruzhansky, Michael; Suragan, Durvudkhan. Local Hardy and Rellich inequalities for sums of squares of vector fields. Adv. Differential Equations 22 (2017), no. 7/8, 505--540. https://projecteuclid.org/euclid.ade/1493863420


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