Lectures on Elliptic Partial Differential Equations

• Main Authors: Ambrosio, Luigi (Author, http://id.loc.gov/vocabulary/relators/aut), Carlotto, Alessandro (http://id.loc.gov/vocabulary/relators/aut), Massaccesi, Annalisa (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Pisa : Scuola Normale Superiore : Imprint: Edizioni della Normale, 2018.
• Edition: 1st ed. 2018.
• Series: Lecture Notes (Scuola Normale Superiore) ; 18
• Subjects: Partial differential equations.; Calculus of variations.; Partial Differential Equations.; Calculus of Variations and Optimal Control; Optimization.

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 reg...

Table of Contents:

• Variational aspects of some classes of elliptic problems
• Classical regularity theory for linear problems
• Interior regularity for nonlinear equations
• Regularity for systems
• Viscosity solutions
• Appendices - A. Some basic facts concerning Sobolev spaces
• B. Miscellaneous results in real and harmonic analysis
• C. Hausdorff measures
• D. Some tools from convex and nonsmooth analysis.