000			02112 a2200241 4500
008			240615b |||||||| |||| 00| 0 eng d
020			_a9781470476250
082			_a515.3533 LEN
100			_aLe, Nam Q.
245			_aAnalysis of Monge–Ampère equations
260			_aProvidence, Rhode Island: _bAmerican Mathematical Society, _c2024.
300			_axx, 576p.: _bpbk.: _c25cm.
440			_aGraduate Studies in Mathematics, V. 240
504			_aInclude bibliography & index.
520			_aThis book presents a systematic analysis of the Monge–Ampère equation, the linearized Monge–Ampère equation, and their applications, with emphasis on both interior and boundary theories. Starting from scratch, it gives an extensive survey of fundamental results, essential techniques, and intriguing phenomena in the solvability, geometry, and regularity of Monge–Ampère equations. It describes in depth diverse applications arising in geometry, fluid mechanics, meteorology, economics, and the calculus of variations. The modern treatment of boundary behaviors of solutions to Monge–Ampère equations, a very important topic of the theory, is thoroughly discussed. The book synthesizes many important recent advances, including Savin's boundary localization theorem, spectral theory, and interior and boundary regularity in Sobolev and Hölder spaces with optimal assumptions. It highlights geometric aspects of the theory and connections with adjacent research areas. This self-contained book provides the necessary background and techniques in convex geometry, real analysis, and partial differential equations, presents detailed proofs of all theorems, explains subtle constructions, and includes well over a hundred exercises. It can serve as an accessible text for graduate students as well as researchers interested in this subject. https://bookstore.ams.org/GSM-240
650			_aConvex
650			_aDiscrete Geometry
650			_aPartial Differential Equations
650			_aGeometry
650			_aBoundary Localization
650			_aViscosity Solutions
942			_cTD _2ddc
999			_c60022 _d60022