Blow-up Theory for Elliptic PDEs in Riemannian Geometry
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A01=Emmanuel Hebey
A01=Frederic Robert
A01=Olivier Druet
Asymptotic analysis
Author_Emmanuel Hebey
Author_Frederic Robert
Author_Olivier Druet
Category=PBKJ
Category=PBMP
Cayley-Hamilton theorem
Contradiction
Curvature
Diffeomorphism
Differentiable manifold
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Equation
Estimation
Euclidean space
Laplace's equation
Maximum principle
Nonlinear system
Polynomial
Princeton University Press
Result
Ricci curvature
Riemannian geometry
Riemannian manifold
Simply connected space
Sphere theorem (3-manifolds)
Stone's theorem
Submanifold
Subsequence
Theorem
Three-dimensional space (mathematics)
Topology
Unit sphere
Product details
- ISBN 9780691119533
- Weight: 312g
- Dimensions: 152 x 235mm
- Publication Date: 09 May 2004
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
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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.
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.
