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

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

9783319274850 (electronic book)
3319274856 (electronic book)
9783319274843
3319274848

Cham : Springer, 2016.

English

1 online resource (xii, 201 pages).

10.1007/978-3-319-27485-0 doi

QA377

515/.3533

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.

Includes bibliographical references and index.

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Online resource; title from PDF title page (SpringerLink, viewed April 12, 2016).

Lecture notes of the Unione Matematica Italiana ; 19.

Print version: 9783319274843

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