Lectures on Elliptic Partial Differential Equations (Publications of the Scuola Normale Superiore Book 18)

The book originates from the Elliptic PDE course given by the first author at the Scuola Normale Superiore in recent years. It covers the most classical aspects of the theory of Elliptic Partial Differential Equations and Calculus of Variations, including also more recent developments on partial regularity for systems and the theory of viscosity solutions. Front Matter ....Pages i-x Variational aspects of some classes of elliptic problems (Luigi Ambrosio, Alessandro Carlotto, Annalisa Massaccesi)....Pages 1-27 Classical regularity theory for linear problems (Luigi Ambrosio, Alessandro Carlotto, Annalisa Massaccesi)....Pages 29-50 Interior regularity for nonlinear equations (Luigi Ambrosio, Alessandro Carlotto, Annalisa Massaccesi)....Pages 51-98 Regularity for systems (Luigi Ambrosio, Alessandro Carlotto, Annalisa Massaccesi)....Pages 99-122 Viscosity solutions (Luigi Ambrosio, Alessandro Carlotto, Annalisa Massaccesi)....Pages 123-167 Back Matter ....Pages 169-227