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Chapter 1: Preliminaries
https://doi.org/10.1142/9781783265534_0002Cited by:0 (Source: Crossref)
Abstract:
The following sections are included:
Introduction
Continuous and Hölder continuous functions
Space of continuous functions and notations
Hölder continuous functions
Exercises
Lp spaces
Basic definitions and properties
Weak convergence and Riemann-Lebesgue theorem
The fundamental lemma of the calculus of variations
Exercises
Sobolev spaces
Definitions and first properties
Some further properties
Imbeddings and compact imbeddings
Poincaré inequality
Exercises
Convex analysis
Exercises
