Inequalities Based on Sobolev Representations

✍ Scribed by George A. Anastassiou (auth.)

• Publisher: Springer-Verlag New York
• Year: 2011
• Tongue: English
• Leaves: 76
• Series: SpringerBriefs in Mathematics
• Edition: 1
• Category: Library

✦ Synopsis

Inequalities based on Sobolev Representations deals exclusively with very general tight integral inequalities of Chebyshev-Grüss, Ostrowski types and of integral means, all of which depend upon the Sobolev integral representations of functions. Applications illustrate inequalities that engage in ordinary and weak partial derivatives of the involved functions. This book also derives important estimates for the averaged Taylor polynomials and remainders of Sobolev integral representations. The results are examined in all directions and through both univariate and multivariate cases. This book is suitable for researchers, graduate students, and seminars in subareas of mathematical analysis, inequalities, partial differential equations and information theory.

✦ Table of Contents

Front Matter....Pages i-ix
Univariate Integral Inequalities Based on Sobolev Representations....Pages 1-34
Multivariate Integral Inequalities Deriving from Sobolev Representations....Pages 35-65

✦ Subjects

Real Functions; Statistics, general; Engineering Design