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Compactness and Stability for Nonlinear Elliptic Equations
Emmanuel Hebey, Université de Cergy-Pontoise, France
A publication of the European Mathematical Society.
Zurich Lectures in Advanced Mathematics
2014; 301 pp; softcover
Volume: 20
ISBN-10: 3-03719-134-1
ISBN-13: 978-3-03719-134-7
List Price: US$52
Member Price: US$41.60
Order Code: EMSZLEC/20
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The book offers an expanded version of lectures given at ETH Zürich in the framework of a Nachdiplomvorlesung. Compactness and stability for nonlinear elliptic equations in the inhomogeneous context of closed Riemannian manifolds are investigated. This field is presently undergoing great development.

The author describes blow-up phenomena and presents the progress made over the past years on the subject, giving an up-to-date description of the new ideas, concepts, methods, and theories in the field. Special attention is devoted to the nonlinear stationary Schrödinger equation and to its critical formulation.

Intended to be as self-contained as possible, the book is accessible to a broad audience of readers, including graduate students and researchers.

A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.


Graduate students and research mathematicians interested in blow-up theory, compactness, critical nonlinear elliptic equations, and stability.

Table of Contents

  • Some model equations
  • Basic variational methods
  • The \(L^{p}\) and \(H^{1}\)-theories for blow-up
  • Blowing-up solutions in the critical case
  • An introduction to elliptic stability
  • Bounded stability
  • The \(C^{0}\)-theory for blow-up
  • Analytic stability
  • Bibliography
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