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Elliptic Regularity Theory - A First Course (Paperback, 1st ed. 2016)
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Elliptic Regularity Theory - A First Course (Paperback, 1st ed. 2016)
Series: Lecture Notes of the Unione Matematica Italiana, 19
Expected to ship within 10 - 15 working days
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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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