Modern Methods in the Calculus of Variations: Lp Spaces

• Main Authors: Fonseca, Irene (Author), Leoni, Giovanni (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York, 2007.
• Series: Springer Monographs in Mathematics,
• Subjects: Physics.; Mathematical analysis.; Analysis (Mathematics).; Partial differential equations.; Applied mathematics.; Engineering mathematics.; Calculus of variations.; Continuum mechanics.; Physics, general.; Calculus of Variations and Optimal Control; Optimization.; Continuum Mechanics and Mechanics of Materials.; Applications of Mathematics.; Partial Differential Equations.; Analysis.

This is the first of two books on methods and techniques in the calculus of variations. Contemporary arguments are used throughout the text to streamline and present in a unified way classical results, and to provide novel contributions at the forefront of the theory. This book addresses fundamental...

Table of Contents:

• Measure Theory and Lp Spaces
• Measures
• Lp Spaces
• The Direct Method and Lower Semicontinuity
• The Direct Method and Lower Semicontinuity
• ConvexAnalysis
• Functionals Defined on Lp
• Integrands f = f (z)
• Integrands f = f (x, z)
• Integrands f = f (x, u, z)
• Young Measures.