Title: Compactness and stability for nonlinear elliptic equations
Description: 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, 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.
Subjects: Elliptic Differential equations, Manifolds (Mathematics), Nonlinear Differential equations, Équations différentielles elliptiques, Variétés (Mathématiques), Équations différentielles non linéaires, Differential equations, MATHEMATICS, Calculus, Mathematical Analysis, Nichtlineare elliptische Differentialgleichung, Global analysis, analysis on manifolds, Partial differential equations