Divergence Operator and Related Inequalities (eBook)

Gabriel Acosta, Ricardo G. Durán (Autoren)

eBook Download: PDF

2017 | 1st ed. 2017
XIII, 124 Seiten
Springer New York (Verlag)
978-1-4939-6985-2 (ISBN)

Infos

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.

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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  a 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.

Inhalt

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.

Produkt-Details

• Erscheint lt. Verlag: 1.3.2017
• Reihe/Serie: SpringerBriefs in Mathematics
• Reihe/Serie: SpringerBriefs in Mathematics
• Zusatzinfo: XIII, 124 p. 7 illus.
• Verlagsort: New York
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Mechanik
• Themenwelt: Technik ► Bauwesen
• Themenwelt: Technik ► Maschinenbau
• Schlagworte: Improved Poincare Inequalities • John Domains • Korn's Inequalities • Right Inverse of the Divergence Operator • Singular Domains • weighted Sobolev spaces
• ISBN-10: 1-4939-6985-4 / 1493969854
• ISBN-13: 978-1-4939-6985-2 / 9781493969852