Divergence Operator and Related Inequalities

✍ Scribed by Gabriel Acosta, Ricardo G. Durán (auth.)

• Publisher: Springer-Verlag New York
• Year: 2017
• Tongue: English
• Leaves: 132
• Series: SpringerBriefs in Mathematics
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xiii
Introduction....Pages 1-12
Divergence Operator....Pages 13-45
Korn’s Inequalities....Pages 47-60
Singular Domains....Pages 61-97
Back Matter....Pages 99-124

✦ Subjects

Analysis;Continuum Mechanics and Mechanics of Materials;Classical Mechanics