LEADER 02547nam 22004695a 450 001 9910155397003321 005 20220726200016.0 010 $a3-03719-670-X 024 70$a10.4171/170 035 $a(CKB)3710000000974733 035 $a(CH-001817-3)213-161205 035 $a(PPN)197529194 035 $a(EXLCZ)993710000000974733 100 $a20161205j20170101 fy 0 101 0 $aeng 135 $aurnn#mmmmamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aThe Monge-Ampe?re equation and its applications$b[electronic resource] /$fAlessio Figalli 210 3 $aZuerich, Switzerland $cEuropean Mathematical Society Publishing House$d2017 215 $a1 online resource (210 pages) 225 0 $aZurich Lectures in Advanced Mathematics (ZLAM) 311 $a3-03719-170-8 327 $aIntroduction -- Alexandrov solutions -- Smooth solutions -- Interior regularity of weak solutions -- Further results and extensions 330 $aThe Monge-Ampe?re equation is one of the most important partial differential equations, appearing in many problems in analysis and geometry. This monograph is a comprehensive introduction to the existence and regularity theory of the Monge-Ampe?re equation and some selected applications; the main goal is to provide the reader with a wealth of results and techniques he or she can draw from to understand current research related to this beautiful equation. The presentation is essentially self-contained, with an appendix wherein one can find precise statements of all the results used from different areas (linear algebra, convex geometry, measure theory, nonlinear analysis, and PDEs). This book is intended for graduate students and researchers interested in nonlinear PDEs: explanatory figures, detailed proofs, and heuristic arguments make this book suitable for self-study and also as a reference. 606 $aDifferential equations$2bicssc 606 $aDifferential & Riemannian geometry$2bicssc 606 $aPartial differential equations$2msc 606 $aDifferential geometry$2msc 615 07$aDifferential equations 615 07$aDifferential & Riemannian geometry 615 07$aPartial differential equations 615 07$aDifferential geometry 676 $a515.353 686 $a35-xx$a53-xx$2msc 700 $aFigalli$b Alessio$0756215 801 0$bch0018173 906 $aBOOK 912 $a9910155397003321 996 $aMonge-Ampère equation and its applications$91534926 997 $aUNINA