REFINED RELLICH BOUNDARY INEQUALITIES FOR THE DERIVATIVES OF A HARMONIC FUNCTION

Siddhant Agrawal; Thomas Alazard

doi:10.1090/proc/16277

REFINED RELLICH BOUNDARY INEQUALITIES FOR THE DERIVATIVES OF A HARMONIC FUNCTION

Siddhant Agrawal
, Thomas Alazard

ICMAT, CSIC-UAM-UC3M-UCM

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

Abstract

The classical Rellich inequalities imply that the L²-norms of the normal and tangential derivatives of a harmonic function are equivalent. In this note, we prove several refined inequalities, which make sense even if the domain is not Lipschitz. For two-dimensional domains, we obtain a sharp L^p-estimate for 1 < p ≤ 2 by using a Riemann mapping and interpolation argument.

Original language	English
Pages (from-to)	2103-2113
Number of pages	11
Journal	Proceedings of the American Mathematical Society
Volume	151
Issue number	5
DOIs	https://doi.org/10.1090/proc/16277
Publication status	Published - 1 May 2023
Externally published	Yes

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title = "REFINED RELLICH BOUNDARY INEQUALITIES FOR THE DERIVATIVES OF A HARMONIC FUNCTION",

abstract = "The classical Rellich inequalities imply that the L2-norms of the normal and tangential derivatives of a harmonic function are equivalent. In this note, we prove several refined inequalities, which make sense even if the domain is not Lipschitz. For two-dimensional domains, we obtain a sharp Lp-estimate for 1 < p ≤ 2 by using a Riemann mapping and interpolation argument.",

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AB - The classical Rellich inequalities imply that the L2-norms of the normal and tangential derivatives of a harmonic function are equivalent. In this note, we prove several refined inequalities, which make sense even if the domain is not Lipschitz. For two-dimensional domains, we obtain a sharp Lp-estimate for 1 < p ≤ 2 by using a Riemann mapping and interpolation argument.

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M3 - Article

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JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

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REFINED RELLICH BOUNDARY INEQUALITIES FOR THE DERIVATIVES OF A HARMONIC FUNCTION

Abstract

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