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These lecture notes provide a self-contained introduction to regularity theory for elliptic equations and systems in divergence form. After a short review of some classical results on everywhere regularity for scalar-valued weak solutions, the presentation focuses on vector-valued weak solutions to a system of several coupled equations.
Preliminaries.- Introduction to the Setting.- The Scalar Case.- Foundations for the Vectorial Case.- Partial Regularity Results for Quasilinear Systems.
“The whole text is equipped with many useful and interesting remarks, which helps make the lecture notes very readable. The book seems to be a solid contribution to understanding the problems of the regularity theory.” (Eugen Viszus, Mathematical Reviews, March, 2017)
Luigi Ambrosio, Gianluca Crippa, Camillo De Lellis, Felix Otto, Michael Westdickenberg, Fabio Ancona, Stefano Bianchini, Rinaldo M. Colombo, Camillo De Lellis, Andrea Marson, Annamaria Montanari