Isoperimetric inequality for div-curl fields

Isoperimetric inequality for div-curl fields

<p/> <p>Let <inline-formula><graphic file="1029-242X-2002-458673-i1.gif"/></inline-formula> be a H&#246;lder conjugate pair of vector fields, both belonging to the space <inline-formula><graphic file="1029-242X-2002-458673-i2.gif"/>&l...

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Bibliographic Details
Main Authors: di Napoli Antonia Passarelli, Carozza Menita
Format: Article
Language:English
Published: SpringerOpen 2002-01-01
Series:Journal of Inequalities and Applications
Subjects:
Isoperimetric inequality
Div-curl fields
H&#246;lder continuity
Online Access:http://www.journalofinequalitiesandapplications.com/content/7/458673
Description
Summary:<p/> <p>Let <inline-formula><graphic file="1029-242X-2002-458673-i1.gif"/></inline-formula> be a H&#246;lder conjugate pair of vector fields, both belonging to the space <inline-formula><graphic file="1029-242X-2002-458673-i2.gif"/></inline-formula>. Suppose that div <inline-formula><graphic file="1029-242X-2002-458673-i3.gif"/></inline-formula> and curl <inline-formula><graphic file="1029-242X-2002-458673-i4.gif"/></inline-formula>. In this paper we prove the following isoperimetric type inequality <inline-formula><graphic file="1029-242X-2002-458673-i5.gif"/></inline-formula> where <inline-formula><graphic file="1029-242X-2002-458673-i6.gif"/></inline-formula> and <inline-formula><graphic file="1029-242X-2002-458673-i7.gif"/></inline-formula>. As an application, we recover H&#246;lder continuity for solutions of n-Laplace equation <inline-formula><graphic file="1029-242X-2002-458673-i8.gif"/></inline-formula>.</p>
ISSN:1025-5834
1029-242X

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