WEAK VECTOR AND SCALAR POTENTIALS: APPLICATIONS TO POINCARÉ'S THEOREM AND KORN'S INEQUALITY IN SOBOLEV SPACES WITH NEGATIVE EXPONENTS-Reference-Cited by-同舟云学术

WEAK VECTOR AND SCALAR POTENTIALS: APPLICATIONS TO POINCARÉ'S THEOREM AND KORN'S INEQUALITY IN SOBOLEV SPACES WITH NEGATIVE EXPONENTS

Published:2010-01 Issue:01 Volume:08 Page:1-17
ISSN:0219-5305
Container-title:Analysis and Applications
language:en
Short-container-title:Anal. Appl.

Author:

AMROUCHE CHÉRIF¹,CIARLET PHILIPPE G.²,CIARLET PATRICK³

Affiliation:

1. Laboratoire de Mathématiques Appliquées, UMR 5142 CNRS, Université de Pau et des Pays de l'Adour, IPRA, Avenue de l'Université, 64000 Pau, France

2. Department of Mathematics, City University of Hong Kong, 83, Tat Chee Avenue, Kowloon, Hong Kong

3. Laboratoire POEMS, UMR 7231 CNRS/ENSTA/INRIA, École Nationale Supérieure de Techniques Avancées, 32, Boulevard Victor, 75739 Paris Cedex 15, France

Abstract

In this paper, we present several results concerning vector potentials and scalar potentials with data in Sobolev spaces with negative exponents, in a not necessarily simply-connected, three-dimensional domain. We then apply these results to Poincaré's theorem and to Korn's inequality.

Publisher

World Scientific Pub Co Pte Ltd

Subject

Applied Mathematics,Analysis

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219530510001497

Reference12 articles.

1. Vector potentials in three-dimensional non-smooth domains

2. Vector and scalar potentials, Poincaré's theorem and Korn's inequality

3. On the characterizations of matrix fields as linearized strain tensor fields

4. Decomposition of vector spaces and application to the Stokes problem in arbitrary dimension

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