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Elliptic regularity theory[electroni...

Beck, Lisa.

Elliptic regularity theory[electronic resource] :a first course /

レコード種別:	言語・文字資料 (印刷物) : 単行資料
[NT 15000414] null:	515.3533
タイトル / 著者:	Elliptic regularity theory : a first course // by Lisa Beck.
著者:	Beck, Lisa.
出版された:	Cham : : Springer International Publishing :, 2016.
記述:	xii, 201 p. : : ill., digital ;; 24 cm.
含まれています:	Springer eBooks
主題:	Differential equations, Elliptic.
主題:	Analytic functions.
主題:	Mathematics.
主題:	Partial Differential Equations.
主題:	Calculus of Variations and Optimal Control; Optimization.
国際標準図書番号 (ISBN) :	9783319274850
国際標準図書番号 (ISBN) :	9783319274843
[NT 15000228] null:	Preliminaries -- Introduction to the Setting -- The Scalar Case -- Foundations for the Vectorial Case -- Partial Regularity Results for Quasilinear Systems.
[NT 15000229] null:	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.
電子資源:	http://dx.doi.org/10.1007/978-3-319-27485-0

Elliptic regularity theory[electronic resource] :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:

393850
Differential equations, Elliptic.

LC Class. No.: QA377

Dewey Class. No.: 515.3533

Elliptic regularity theory[electronic resource] :a first course /
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245 1 0 $a Elliptic regularity theory $h [electronic resource] : $b a first course / $c by Lisa Beck.
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300 $a xii, 201 p. : $b ill., digital ; $c 24 cm.
490 1 $a Lecture notes of the Unione Matematica Italiana, $x 1862-9113 ; $v 19
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.
650 0 $a Differential equations, Elliptic. $3 393850
650 0 $a Analytic functions. $3 470209
650 1 4 $a Mathematics. $3 172349
650 2 4 $a Partial Differential Equations. $3 464931
650 2 4 $a Calculus of Variations and Optimal Control; Optimization. $3 464715
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950 $a Mathematics and Statistics (Springer-11649)

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