Zurich Lectures in Advanced Mathematics Edited by Erwin Bolthausen (Managing Editor), Freddy Delbaen, Thomas Kappeler (Managing Editor), Christoph Schwab, Michael Struwe, Gisbert Wüstholz Mathematics in Zurich has a long and distinguished tradition, in which the writing of lecture notes volumes and research monographs plays a prominent part. The Zurich Lectures in Advanced Mathematics series aims to make some of these publications better known to a wider audience. The series has three main constituents: lecture notes on advanced topics given by internationally renowned experts, in particular lecture notes of "Nachdiplomvorlesungen", organzied jointly by the Department of Mathematics and the Institute for Research in Mathematics (FIM) at ETH, graduate text books designed for the joint graduate program in Mathematics of the ETH and the University of Zürich, as well as contributions from researchers in residence. Moderately priced, concise and lively in style, the volumes of this series will appeal to researchers and students alike, who seek an informed introduction to important areas of current research. Previously published in this series: Yakov B. Pesin, Lectures on partial hyperbolicity and stable ergodicity Sun-Yung Alice Chang, Non-linear Elliptic Equations in Conformal Geometry Sergei B. Kuksin, Randomly forced nonlinear PDEs and statistical hydrodynamics in 2 space dimensions Pavel Etingof, Calogero-Moser systems and representation theory Guus Balkema and Paul Embrechts, High Risk Scenarios and Extremes – A geometric approach Demetrios Christodoulou, Mathematical Problems of General Relativity I Camillo De Lellis, Rectifiable Sets, Densities and Tangent Measures Paul Seidel, Fukaya Categories and Picard–Lefschetz Theory Alexander H.W. Schmitt, Geometric Invariant Theory and Decorated Principal Bundles Michael Farber, Invitation to Topological Robotics Alexander Barvinok, Integer Points in Polyhedra Christian Lubich, From Quantum to Classical Molecular Dynamics: Reduced Models and Numerical Analysis Shmuel Onn, Nonlinear Discrete Optimization – An Algorithmic Theory Kenji Nakanishi and Wilhelm Schlag, Invariant Manifolds and Dispersive Hamiltonian Evolution Equations Erwan Faou, Geometric Numerical Integration and Schrödinger Equations Alain-Sol Sznitman, Topics in Occupation Times and Gaussian Free Fields François Labourie, Lectures on Representations of Surface Groups Isabelle Gallagher, Laure Saint-Raymond and Benjamin Texier, From Newton to Boltzmann: Hard Spheres and Short-range Potentials Robert J. Marsh, Lecture Notes on Cluster Algebras Published with the support of the Huber-Kudlich-Stiftung, Zürich
Emmanuel Hebey
Compactness and Stability for Nonlinear Elliptic Equations
Author: Emmanuel Hebey Département de Mathématiques Université de Cergy-Pontoise Site de Saint-Martin 2, avenue Adolphe Chauvin 95302 Cergy-Pontoise cedex France E-mail:
[email protected]
2010 Mathematics S