LEADER 03375nam 22006255 450 001 9910254073203321 005 20250609110031.0 010 $a3-319-27485-6 024 7 $a10.1007/978-3-319-27485-0 035 $a(CKB)3710000000636330 035 $a(EBL)4501069 035 $a(SSID)ssj0001665953 035 $a(PQKBManifestationID)16455244 035 $a(PQKBTitleCode)TC0001665953 035 $a(PQKBWorkID)15000541 035 $a(PQKB)10569359 035 $a(DE-He213)978-3-319-27485-0 035 $a(MiAaPQ)EBC4501069 035 $a(PPN)193444690 035 $a(MiAaPQ)EBC6241798 035 $a(EXLCZ)993710000000636330 100 $a20160408d2016 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aElliptic regularity theory $ea first course /$fby Lisa Beck 205 $a1st ed. 2016. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016. 215 $a1 online resource (214 p.) 225 1 $aLecture Notes of the Unione Matematica Italiana,$x1862-9113 ;$v19 300 $aDescription based upon print version of record. 311 08$a3-319-27484-8 320 $aIncludes bibliographical references and index. 327 $aPreliminaries -- Introduction to the Setting -- The Scalar Case -- Foundations for the Vectorial Case -- Partial Regularity Results for Quasilinear Systems. 330 $aThese lecture notes provide a self-contained introduction to regularity theory for elliptic equations and systems in divergence form. After a short review of some classical results on everywhere regularity for scalar-valued weak solutions, the presentation focuses on vector-valued weak solutions to a system of several coupled equations. In the vectorial case, weak solutions may have discontinuities and so are expected, in general, to be regular only outside of a set of measure zero. Several methods are presented concerning the proof of such partial regularity results, and optimal regularity is discussed. Finally, a short overview is given on the current state of the art concerning the size of the singular set on which discontinuities may occur. The notes are intended for graduate and postgraduate students with a solid background in functional analysis and some familiarity with partial differential equations; they will also be of interest to researchers working on related topics. 410 0$aLecture Notes of the Unione Matematica Italiana,$x1862-9113 ;$v19 606 $aDifferential equations, Partial 606 $aCalculus of variations 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aCalculus of Variations and Optimal Control; Optimization$3https://scigraph.springernature.com/ontologies/product-market-codes/M26016 615 0$aDifferential equations, Partial. 615 0$aCalculus of variations. 615 14$aPartial Differential Equations. 615 24$aCalculus of Variations and Optimal Control; Optimization. 676 $a515.353 700 $aBeck$b Lisa$4aut$4http://id.loc.gov/vocabulary/relators/aut$0755900 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254073203321 996 $aElliptic regularity theory$91523292 997 $aUNINA