Functional Analysis, Sobolev Spaces, and Calculus of Variations

This book aims at introducing students into the modern analytical foundations to treat problems and situations in the Calculus of Variations solidly and rigorously. Since no background is taken for granted or assumed, as the textbook pretends to be self-contained, areas like basic Functional Analysi...

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Bibliographic Details
Main Author: Pedregal, Pablo
Format: eBook
Language:English
Published: Cham Springer Nature Switzerland 2024, 2024
Edition:1st ed. 2024
Series:La Matematica per il 3+2
Subjects:
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
Table of Contents:
  • 1 Motivation and perspective
  • Part I: Basic Functional Analysis and Calculus of Variations
  • 2 A first exposure to Functional Analysis
  • 3 Introduction to convex analysis. The Hahn-Banach and Lax-Milgram theorems
  • 4 The Calculus of Variations for one-dimensional problems
  • Part II: Basic Operator Theory
  • 5 Continuous operators
  • 6 Compact operators
  • Part III: Multidimensional Sobolev Spaces and Scalar Variational Problems
  • 7 Multidimensional Sobolev spaces
  • 8 Variational problems
  • 9 Finer results in Sobolev spaces and the Calculus of Variations
  • Appendix A: Hints and solutions to exercises
  • Appendix B: So much to learn