Partial Differential Equations And The Calculus of Variations

The study of qualitative aspects of PDE's has always attracted much attention from the early beginnings. More recently, once basic issues about PDE's, such as existence, uniqueness and stability of solutions, have been understood quite well, research on topological and/or geometric properties of their solutions has become more intense.

This book is an introduction to the regularity theory for free boundary problems. The focus is on the one-phase Bernoulli problem, which is of particular interest as it deeply influenced the development of the modern free boundary regularity theory and is still an object of intensive research.

The study of qualitative aspects of PDE's has always attracted much attention from the early beginnings. More recently, once basic issues about PDE's, such as existence, uniqueness and stability of solutions, have been understood quite well, research on topological and/or geometric properties of their solutions has become more intense. The study of these issues is attracting the interest of an increasing number of researchers and is now a broad and well-established research area, with contributions that often come from experts from disparate areas of mathematics, such as differential and convex geometry, functional analysis, calculus of variations, mathematical physics, to name a few.

by Thomas Carraro (Editor), Michael Geiger (Editor), Stefan Körkel (Editor), Rolf Rannacher (Editor)

Authors: Bucur, Claudia, Valdinoci, Enrico
Gives a rich introduction to the fractional Laplacian and its applications
Well explained, self-contained and easy to follow, even for those who are not familiar with the subject
Contains brand new and interesting research trends on the fractional Laplacian