Zurich Lectures in Advanced Mathematics 2014; 301 pp; softcover Volume: 20 ISBN10: 3037191341 ISBN13: 9783037191347 List Price: US$52 Member Price: US$41.60 Order Code: EMSZLEC/20
 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 blowup phenomena and presents the progress made over the past years on the subject, giving an uptodate 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 selfcontained 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. Readership Graduate students and research mathematicians interested in blowup 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 blowup
 Blowingup solutions in the critical case
 An introduction to elliptic stability
 Bounded stability
 The \(C^{0}\)theory for blowup
 Analytic stability
 Bibliography
