Sharp remainder of the poincarÉ inequality

Tohru Ozawa; Durvudkhan Suragan

doi:10.1090/proc/15119

Sharp remainder of the poincarÉ inequality

Tohru Ozawa
, Durvudkhan Suragan

Waseda University

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

In this paper, we obtain a sharp remainder formula for the Poincaré inequality which implies a simple proof of the sharp Poincaré inequality without using the variational principle. We also extend the idea to general Carnot groups. Thus, we have succeeded in finding a simple proof of the sharp Poincaré inequality in a more general case.

Original language	English
Pages (from-to)	4235-4239
Number of pages	5
Journal	Proceedings of the American Mathematical Society
Volume	148
Issue number	10
DOIs	https://doi.org/10.1090/proc/15119
Publication status	Published - Oct 2020

Funding

Received by the editors October 24, 2019. 2010 Mathematics Subject Classification. Primary 39B62, 39B99, 22E30. Key words and phrases. Poincaré inequality, sharp remainder, optimal constant, Heisenberg group, Carnot group. The authors were supported in parts by the Nazarbayev University program 091019CRP2120 and the Nazarbayev University grant 240919FD3901. No new data was collected or generated during the course of this research.

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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title = "Sharp remainder of the poincar{\'E} inequality",

abstract = "In this paper, we obtain a sharp remainder formula for the Poincar{\'e} inequality which implies a simple proof of the sharp Poincar{\'e} inequality without using the variational principle. We also extend the idea to general Carnot groups. Thus, we have succeeded in finding a simple proof of the sharp Poincar{\'e} inequality in a more general case.",

author = "Tohru Ozawa and Durvudkhan Suragan",

note = "Funding Information: Received by the editors October 24, 2019. 2010 Mathematics Subject Classification. Primary 39B62, 39B99, 22E30. Key words and phrases. Poincar{\'e} inequality, sharp remainder, optimal constant, Heisenberg group, Carnot group. The authors were supported in parts by the Nazarbayev University program 091019CRP2120 and the Nazarbayev University grant 240919FD3901. No new data was collected or generated during the course of this research. Publisher Copyright: {\textcopyright} 2020 American Mathematical Society Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",

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N2 - In this paper, we obtain a sharp remainder formula for the Poincaré inequality which implies a simple proof of the sharp Poincaré inequality without using the variational principle. We also extend the idea to general Carnot groups. Thus, we have succeeded in finding a simple proof of the sharp Poincaré inequality in a more general case.

AB - In this paper, we obtain a sharp remainder formula for the Poincaré inequality which implies a simple proof of the sharp Poincaré inequality without using the variational principle. We also extend the idea to general Carnot groups. Thus, we have succeeded in finding a simple proof of the sharp Poincaré inequality in a more general case.

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Sharp remainder of the poincarÉ inequality

Abstract

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