On Monge-Ampère type equations arising in optimal transportation problems

DOI10.1007/s00526-006-0045-xzbMath1108.49018OpenAlexW2143223648MaRDI QIDQ866976

Cristian E. Gutiérrez, Van Truyen Nguyen

Publication date: 14 February 2007

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00526-006-0045-x

zbMATH Keywords

maximum principleDirichlet problemcomparison principleAleksandrov principlegeneralized Monge-Ampère measures

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Nonlinear parabolic equations (35K55) Applications of queueing theory (congestion, allocation, storage, traffic, etc.) (60K30)

Related Items (7)

\(L^\infty\)-estimates in optimal transport for non quadratic costs ⋮ Discrete Aleksandrov solutions of the Monge-Ampere equation ⋮ On the classification of symmetry reductions for the \((1+3)\)-dimensional Monge-Ampère equation ⋮ On the Dirichlet problem for Monge-Ampère type equations ⋮ A perturbation argument for a Monge-Ampère type equation arising in optimal transportation ⋮ An Aleksandrov type estimate for ${\alpha }$-convex functions ⋮ On the weak convergence of Monge-Ampère measures for discrete convex mesh functions

Cites Work

• A convexity principle for interacting gases
• The geometry of optimal transportation
• Oblique boundary value problems for equations of Monge-Ampère type
• Regularity of potential functions of the optimal transportation problem
• Zur c-konvexität und c-subdifferenzierbarkelt von funktionalen
• Differential equations methods for the Monge-Kantorovich mass transfer problem
• Variational Analysis
• Zur theorie der polarfunktionale
• The Monge-Ampère equation
• On the Monge mass transfer problem
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