Kommentar |
Themen: Einführung in elementare Eigenschaften konvexer Funktionen • Lösungsbegriffe für die Monge-Ampère-Gleichung • Existenz und Eindeutigkeit von Lösungen des Randwertproblems • Finite-Elemente-Approximation
Vorkenntnisse:
Grundvorlesungen; Kenntnisse zu Differentialgleichungen und aus der Höheren Analysis I können nützlich sein
Literatur:
- A. Figalli, The Monge-Ampère equation and its applications, European Mathematical Society (EMS), Zürich, 2017.
- C. E. Gutiérrez, The Monge-Ampère equation, Birkhäuser/Springer, Cham, 2016, Second edition.
- D. Gallistl, N. T. Tran, Convergence of a regularized finite element discretization of the two-dimensional Monge–Ampère equation, Math. Comp., 2022+. https://arxiv.org/abs/2112.10711
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Topics: Elementary properties of convex functions • solution concepts for the Monge-Ampère equation • existence and uniqueness of solutions for the boundary value problem • finite element approximation
Prerequisites:
Basic lectures; knowledge on differential equations and linear functional analysis can be useful
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