Hebey Emmanuel. Compactness and Stability for Nonlinear Elliptic Equations

European Mathematical Society, 2014. — 301 p. — (Zurich Lectures in Advanced Mathematics 20). — ISBN 978-3-03719-134-7.Компактность и устойчивость нелинейных эллиптических уравненийThe 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, a field 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.Some model equations
Basic variational methods
TheLp and H1-theories for blow-up
Blowing-up solutions in the critical case
An introduction to elliptic stability
Bounded stability
TheC0-theory for blow-up
Analytic stability