An introduction to the regularity theory for elliptic systems, harmonic maps and minimal graphs (Q2920107)

The present volume is a deeply revised edition of the textbook [Zbl 1093.35001] that had grown from lecture notes of a course taught by the first author during the academic year 2003--2004 at the Scuola Normale Superiore di Pisa. It is mainly addressed to students but could be of interest also to working researchers. The authors illustrate some of the relevant ideas and modern issues in the regularity theory of linear and nonlinear elliptic systems. The topics treated in the book include harmonic functions, direct methods in calculus of variations, Hilbert space methods and Sobolev spaces, energy estimates, Schauder and \(L^p\)-theory both with and without potential theory, including the Calderón-Zygmund theorem, Harnack's and De Giorgi-Moser-Nash theorems in the scalar case and partial regularity theorems in the vector valued case, energy minimizing harmonic maps and minimal graphs in codimension 1 and greater than 1.NEWLINENEWLINEIn the second edition they are also include regularity of 2-dimensional weakly harmonic maps, partial regularity of stationary harmonic maps, and their connections with the case \(p=1\) of the \(L^p\)-theory, including the celebrated results of Wente and of Coifman-Lions-Meyer-Semmes.NEWLINENEWLINEThe volume is self-contained and is highly recommended to all researchers working in the field of PDEs.