{"product_id":"9783319274843","title":"Lecture Notes of the Unione Matematica Italiana: A First Course","description":"\u003ch1\u003eLecture Notes of the Unione Matematica Italiana: A First Course\u003c\/h1\u003e \u003ch2\u003eBeck, Lisa\u003c\/h2\u003e \u003cp\u003e\u003c\/p\u003e\u003cp\u003eThese 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.\u003c\/p\u003e  \u003cp\u003eThe 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.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2016-04-18\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9783319274843\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-319-27485-0\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 201\u003c\/p\u003e ","brand":"Springer International Publishing","offers":[{"title":"Default Title","offer_id":45227976360076,"sku":"9783319274843","price":49.49,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783319274843.jpg?v=1775746695","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9783319274843","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}