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arXiv · 1707.03731

Rellich inequalities for sub-Laplacians with drift

Michael Ruzhansky·Nurgissa Yessirkegenov
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Abstract

In this note we prove horizontal weighted Rellich inequalities for the sub-Laplacian and for sub-Laplacians with drift on general stratified groups. We show how the presence of a drift improves the known inequalities. Moreover, we obtain several versions of weighted Rellich inequalities for the sub-Laplacian with drift on the polarizable Carnot groups, also with the weights associated with the fundamental solution of the sub-Laplacian. The obtained results are already new for the Laplacian in the usual Euclidean setting of ${\mathbb R}^n$, embedding the classical Rellich inequality into a family of Rellich inequalities with parameter dependent drifts.

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Michael Ruzhansky, Nurgissa Yessirkegenov. 2017-07-12. Rellich inequalities for sub-Laplacians with drift. https://arxiv.org/abs/1707.03731

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