Blow-up Theory for Elliptic PDEs in Riemannian Geometry (MN-45)
- Avg. Rating:
- Read Review (0)
- Published by: Princeton University Press
- eBook Publish Date: October 30, 2008
- Print ISBN: 0691119538
- Filesize: 16.83 MB
-
List Price: $52.50
You Pay: $52.50
Our eBook Library Software is required to purchase and download eBooks. Download it here.
Overview
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 Schr?dinger 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.
Editorial Reviews
Editorial Reviews for this product are not available at this time.
Author Information
Bio of Olivier Druet
Olivier Druet is Researcher at CNRS, Ecole Normale Superieure de Lyon.
Bio of Emmanuel Hebey
Emmanuel Hebey is Professor at Universite de Cergy-Pontoise. Frederic Robert is Associate Professor at Universite de Nice Sophia-Antipolis.
Customer Reviews
There are no customer reviews available at this time. To add your review, Register or Sign In to your account using our free eBook Library Software.
Additional Info
Imprint
Princeton Univercity Press
Filesize
16.83 MB
Number of Pages
224
eBook ISBN
9781400826162
