Functional Analysis, Sobolev Spaces, and Calculus of Variations

Focusing on the foundational aspects of the Calculus of Variations, this book is designed for students with no prior background, making it self-contained. It begins with essential concepts in Functional Analysis and Sobolev spaces, progressing to one-dimensional variational problems with numerous examples and exercises. The text also covers continuous and compact operators, leading to multi-dimensional Sobolev spaces and complex problems. With a didactic approach, it aims to build a solid understanding, encouraging students to explore more advanced topics in the field.