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The Monge-Ampère equation and its applications Alessio Figalli

By: Figalli, Alessio [VerfasserIn]Material type: TextTextLanguage: English Series: Zurich lectures in advanced mathematicsPublisher: Zürich European Mathematical Society [2017]Description: x, 200 Seiten Illustrationen 24 cmContent type: Text Media type: ohne Hilfsmittel zu benutzen Carrier type: BandISBN: 9783037191705 (kart.)Subject(s): Partielle Differentialgleichung | Nichtlineare elliptische Differentialgleichung | Monge-Ampère equations | Differential equations, Partial | Geometry, Differential | Mathematical physics | Monge-Ampère equationsAdditional physical formats: Erscheint auch als: The Monge-Ampère Equation and Its ApplicationsDDC classification: 515.353 LOC classification: QA377Other classification: 31.45 | SK 560 | SK 950 | mat Online resources: Inhaltsverzeichnis Summary: Introduction -- Alexandrov solutions -- Smooth solutions -- Interior regularity of weak solutions -- Further results and extensionsSummary: "The Monge-Ampère 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-Ampère 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." --
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Literaturverzeichnis: Seite 191-198

Introduction -- Alexandrov solutions -- Smooth solutions -- Interior regularity of weak solutions -- Further results and extensions

"The Monge-Ampère 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-Ampère 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." --

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