Regularity Theory for Elliptic PDE

TL;DR

This book provides an accessible introduction to the regularity theory for elliptic partial differential equations, bridging elementary PDE knowledge and advanced research with a focus on core ideas.

Contribution

It offers a self-contained, comprehensive overview of elliptic PDE regularity theory suitable for students and researchers, emphasizing main concepts over full generality.

Findings

Clarifies key ideas in elliptic PDE regularity

Serves as a bridge between basic and advanced PDE texts

Published as part of Zurich Lectures in Advanced Mathematics

Abstract

This manuscript aims to provide a self-contained introduction to the regularity theory for elliptic PDE, focusing on the main ideas rather than proving all results in their greatest generality. It can be seen as a bridge between an elementary PDE course and more advanced textbooks. This is a draft of the book "Regularity Theory for Elliptic PDE". The final version has been published in Zurich Lectures in Advanced Mathematics, EMS Press, 2022.