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Catalogue Information
Field name	Details
Dewey Class	515.353
Title	Elliptic Regularity Theory ([EBook]) : A First Course / / by Lisa Beck.
Author	Beck, Lisa
Other name(s)	SpringerLink (Online service)
Publication	Cham : : Springer International Publishing : : Imprint: Springer, , 2016.
Physical Details	XII, 201 p. : online resource.
Series	Lecture Notes of the Unione Matematica Italiana 1862-9113 ; ; 19
ISBN	9783319274850
Summary Note	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.:
Contents note	Preliminaries -- Introduction to the Setting -- The Scalar Case -- Foundations for the Vectorial Case -- Partial Regularity Results for Quasilinear Systems.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-319-27485-0
Links to Related Works	Subject References: Calculus of variations . Calculus of variations and optimal control; optimization . Mathematics . Partial differential equations . Authors: Beck, Lisa . Corporate Authors: SpringerLink (Online service) . Series: Lecture Notes of the Unione Matematica Italiana . Classification: 515.353 .

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Elliptic Regularity Theory: A First Course /

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