Elliptic Regularity Theory : A First Course, Beck, Lisa 9783319274843 New<-

Springer International Publishing AG

Elliptic Regularity TheoryA First Course\nAuthor(s): Lisa Beck\nFormat: Paperback\nPublisher: Springer International Publishing AG, Switzerland\nImprint: Springer International Publishing AG\nISBN-13: 9783319274843, 978-3319274843\nSynopsis\nThese 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. In the vectorial case, weak solutions may have discontinuities and so are expected, in general, to be regular only outside of a set of measure zero. Several methods are presented concerning the proof of such partial regularity results, and optimal regularity is discussed. Finally, a short overview is given on the current state of the art concerning the size of the singular set on which discontinuities may occur.\n.