The aim of this book is to introduce the reader to different topics of the theory of elliptic partial differential equations by avoiding technicalities and refi

Semilinear elliptic equations are of fundamental importance for the study of geometry, physics, mechanics, engineering and life sciences. The variational approa

These lecture notes provide a self-contained introduction to regularity theory for elliptic equations and systems in divergence form. After a short review of so

This volume is based on PDE courses given by the authors at the Courant Institute and at the University of Notre Dame, Indiana. Presented are basic methods for