Blow-up Theory for Elliptic PDEs in Riemannian Geometry (MN-45)
(Paperback)
Publishing Details
Blow-up Theory for Elliptic PDEs in Riemannian Geometry (MN-45)
By (Author) Olivier Druet
By (author) Emmanuel Hebey
By (author) Frdric Robert
Princeton University Press
Princeton University Press
19th July 2004
United States
Classifications
Professional and Scholarly
Non Fiction
Differential and Riemannian geometry
515.353
Physical Properties
Paperback
224
Width 152mm, Height 235mm
312g
Description
Elliptic equations of critical Sobolev growth have been the target of investigation for decades because they have proved to be of great importance in analysis, geometry, and physics. The equations studied here are of the well-known Yamabe type. They involve Schrodinger operators on the left hand side and a critical nonlinearity on the right hand side. A significant development in the study of such equations occurred in the 1980s. It was discovered that the sequence splits into a solution of the limit equation - a finite sum of bubbles - and a rest that converges strongly to zero in the Sobolev space consisting of square integrable functions whose gradient is also square integrable. This splitting is known as the integral theory for blow-up. In this book, the authors develop the pointwise theory for blow-up. They introduce new ideas and methods that lead to sharp pointwise estimates. These estimates have important applications when dealing with sharp constant problems (a case where the energy is minimal) and compactness results (a case where the energy is arbitrarily large). The authors carefully and thoroughly describe pointwise behavior when the energy is arbitrary. Intended to be as self-contained as possible, this accessible book will interest graduate students and researchers in a range of mathematical fields.
Reviews
"This is an important and original work. It develops critical new ideas and methods for the analysis of elliptic PDEs on compact manifolds, especially in the framework of the Yamabe equation, critical Sobolev embedding, and blow-up techniques. This volume will have an important influence on current research."William Beckner, University of Texas at Austin
Author Bio
Olivier Druet is Researcher at CNRS, Ecole Normale Superieure de Lyon. Emmanuel Hebey is Professor at Universite de Cergy-Pontoise. Frederic Robert is Associate Professor at Universite de Nice Sophia-Antipolis.
