Past lectures

Abstract

This series of lectures is devoted to the study of compactness and elliptic stability for nonlinear elliptic equations in the inhomogeneous context of closed Riemannian manifolds. We describe blow-up phenomena from the Lebesgue theory to the pointwise theory, and discuss the progress made in the field over the past years.

Special attention will be devoted to the model case of the nonlinear stationary Schrödinger equation and to its critical formulation. Other important models will be discussed.