Compactness and Stability for Nonlinear Elliptic Equations

The book offers an expanded version of lectures given at ETH Zurich 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...
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The book offers an expanded version of lectures given at ETH Zurich 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 Schrodinger 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.