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Divergence operator and related ineq...

Acosta, Gabriel.

Divergence operator and related inequalities

Record Type:	Electronic resources : Monograph/item
Title/Author:	Divergence operator and related inequalitiesby Gabriel Acosta, Ricardo G. Duran.
Author:	Acosta, Gabriel.
other author:	Duran, Ricardo G.
Published:	New York, NY :Springer New York :2017.
Description:	xiii, 124 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Inequalities (Mathematics)
Online resource:	http://dx.doi.org/10.1007/978-1-4939-6985-2
ISBN:	9781493969852$q(electronic bk.)

Divergence operator and related inequalities
Acosta, Gabriel.

Divergence operator and related inequalities[electronic resource] /by Gabriel Acosta, Ricardo G. Duran. - New York, NY :Springer New York :2017. - xiii, 124 p. :ill., digital ;24 cm. - SpringerBriefs in mathematics,2191-8198. - SpringerBriefs in mathematics..

Introduction -- Divergence Operator -- Korn's Inequalities -- Singular Domains -- Basic Equations of Continuum Mechanics -- Powers of the Distance to the Boundary as Ap Weights -- An Auxiliary Result on Holder a Domains.

This Brief is mainly devoted to two classical and related results: the existence of a right inverse of the divergence operator and the so-called Korn Inequalities. It is well known that both results are fundamental tools in the analysis of some classic differential equations, particularly in those arising in fluid dynamics and elasticity. Several connections between these two topics and improved Poincare inequalities are extensively treated. From simple key ideas the book is growing smoothly in complexity. Beginning with the study of these problems on star-shaped domains the arguments are extended first to John domains and then to Holder α domains where the need of weighted spaces arises naturally. In this fashion, the authors succeed in presenting in an unified and concise way several classic and recent developments in the field. These features certainly makes this Brief useful for students, post-graduate students, and researchers as well.

ISBN: 9781493969852$q(electronic bk.)

Standard No.: 10.1007/978-1-4939-6985-2doiSubjects--Topical Terms:

183909
Inequalities (Mathematics)

LC Class. No.: QA295

Dewey Class. No.: 515.26

Divergence operator and related inequalities
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245 1 0 $a Divergence operator and related inequalities $h [electronic resource] / $c by Gabriel Acosta, Ricardo G. Duran.
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505 0 $a Introduction -- Divergence Operator -- Korn's Inequalities -- Singular Domains -- Basic Equations of Continuum Mechanics -- Powers of the Distance to the Boundary as Ap Weights -- An Auxiliary Result on Holder a Domains.
520 $a This Brief is mainly devoted to two classical and related results: the existence of a right inverse of the divergence operator and the so-called Korn Inequalities. It is well known that both results are fundamental tools in the analysis of some classic differential equations, particularly in those arising in fluid dynamics and elasticity. Several connections between these two topics and improved Poincare inequalities are extensively treated. From simple key ideas the book is growing smoothly in complexity. Beginning with the study of these problems on star-shaped domains the arguments are extended first to John domains and then to Holder α domains where the need of weighted spaces arises naturally. In this fashion, the authors succeed in presenting in an unified and concise way several classic and recent developments in the field. These features certainly makes this Brief useful for students, post-graduate students, and researchers as well.
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