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Elliptic regularity theory = a first course /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Elliptic regularity theory/ by Lisa Beck.
Reminder of title:	a first course /
Author:	Beck, Lisa.
Published:	Cham :Springer International Publishing : : 2016.,
Description:	xii, 201 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
Subject:	Differential equations, Elliptic. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-27485-0
ISBN:	9783319274850

Elliptic regularity theory = a first course /
Beck, Lisa.

Elliptic regularity theorya first course /[electronic resource] :by Lisa Beck. - Cham :Springer International Publishing :2016. - xii, 201 p. :ill., digital ;24 cm. - Lecture notes of the Unione Matematica Italiana,191862-9113 ;. - Lecture notes of the Unione Matematica Italiana ;16..

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.

ISBN: 9783319274850

Standard No.: 10.1007/978-3-319-27485-0doiSubjects--Topical Terms:

563985
Differential equations, Elliptic.

LC Class. No.: QA377

Dewey Class. No.: 515.3533

Elliptic regularity theory = a first course /
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505 0 $a Preliminaries -- Introduction to the Setting -- The Scalar Case -- Foundations for the Vectorial Case -- Partial Regularity Results for Quasilinear Systems.
520 $a 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.
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650 1 4 $a Mathematics. $3 527692
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