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＜E-Book＞
Elliptic Regularity Theory : A First Course / by Lisa Beck
(Lecture Notes of the Unione Matematica Italiana. ISSN:18629121 ; 19)

Edition	1st ed. 2016.
Publisher	(Cham : Springer International Publishing : Imprint: Springer)
Year	2016
Size	XII, 201 p : online resource
Authors	*Beck, Lisa author SpringerLink (Online service)
Subjects	LCSH:Differential equations LCSH:Mathematical optimization LCSH:Calculus of variations FREE:Differential Equations FREE:Calculus of Variations and Optimization
Notes	Preliminaries -- Introduction to the Setting -- The Scalar Case -- Foundations for the Vectorial Case -- Partial Regularity Results for Quasilinear Systems 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. 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. The notes are intended for graduate and postgraduate students with a solid background in functional analysis and some familiarity with partial differential equations; they will also be of interest to researchers working on related topics HTTP:URL=https://doi.org/10.1007/978-3-319-27485-0

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