Divergence operator and related inequalities / by Gabriel Acosta, Ricardo G. Durán.

Format:

Book

Author/Creator:

Acosta, Gabriel., Author.

Durán, Ricardo G., Author.

Series:

SpringerBriefs in Mathematics, 2191-8198

Language:

English

Subjects (All):

Mathematical analysis.

Mechanics.

Mechanics, Applied.

Analysis.

Solid Mechanics.

Classical Mechanics.

Local Subjects:

Analysis.

Solid Mechanics.

Classical Mechanics.

Physical Description:

1 online resource (XIII, 124 p. 7 illus.)

Edition:

1st ed. 2017.

Place of Publication:

New York, NY : Springer New York : Imprint: Springer, 2017.

Summary:

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 Poincaré 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 Hölder 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.

Contents:

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.

Notes:

Includes bibliographical references and index.