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Without convexity: Loss of uniqueness
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Classroom Contents
Convergent Semi-Lagrangian Methods for the Monge-Ampère Equation on Unstructured Grids
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- 1 Intro
- 2 The outline
- 3 Motivation: Optimal transport
- 4 Motivation: Inverse reflector problem
- 5 Simple Monge Ampere equation
- 6 Ellipticity and convexity
- 7 Without convexity: Loss of uniqueness
- 8 Viscosity solution of the Monge Ampere equation
- 9 Summary of Part 1
- 10 Classical equivalence
- 11 Viscosity solutions of HJB
- 12 Equivalence in viscosity sense
- 13 Comparison principle
- 14 Summary of Part 2
- 15 Summary of Part 3
- 16 Towards convergence
- 17 How should we pose boundary conditions?
- 18 Summary of Part 4
- 19 Two numerical experiments
- 20 Summary of the presentation
