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

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

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.

langue originale	Anglais
Pages (de - à)	2103-2113
Nombre de pages	11
journal	Proceedings of the American Mathematical Society
Volume	151
Numéro de publication	5
Les DOIs	https://doi.org/10.1090/proc/16277
état	Publié - 1 mai 2023
Modification externe	Oui

Accès au document

10.1090/proc/16277

Autres fichiers et liens

Lien vers la publication dans Scopus

Contient cette citation

@article{237fd8adf8e742e89d262d7135732e45,

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.",

author = "Siddhant Agrawal and Thomas Alazard",

note = "Publisher Copyright: {\textcopyright} 2023 American Mathematical Society.",

year = "2023",

month = may,

day = "1",

doi = "10.1090/proc/16277",

language = "English",

volume = "151",

pages = "2103--2113",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

number = "5",

}

TY - JOUR

T1 - REFINED RELLICH BOUNDARY INEQUALITIES FOR THE DERIVATIVES OF A HARMONIC FUNCTION

AU - Agrawal, Siddhant

AU - Alazard, Thomas

PY - 2023/5/1

Y1 - 2023/5/1

N2 - 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.

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.

UR - https://www.scopus.com/pages/publications/85150222965

U2 - 10.1090/proc/16277

DO - 10.1090/proc/16277

M3 - Article

AN - SCOPUS:85150222965

SN - 0002-9939

VL - 151

SP - 2103

EP - 2113

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 5

ER -

REFINED RELLICH BOUNDARY INEQUALITIES FOR THE DERIVATIVES OF A HARMONIC FUNCTION

Résumé

Accès au document

Autres fichiers et liens

Empreinte digitale

Contient cette citation