Optimal Transportation with Boundary Costs and Summability Estimates on the Transport Density

zbMath1391.35093arXiv1609.08418MaRDI QIDQ4609980

Samer Dweik

Publication date: 27 March 2018

Full work available at URL: https://arxiv.org/abs/1609.08418

zbMATH Keywords

Dirichlet boundary conditionsshape optimizationMonge-Kantorovich equation

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Boundary value problems for second-order elliptic equations (35J25) Regularity of solutions in optimal control (49N60) Applications of functional analysis in optimization, convex analysis, mathematical programming, economics (46N10)

Related Items (7)

\( W^{1, p}\) regularity on the solution of the BV least gradient problem with Dirichlet condition on a part of the boundary ⋮ Weighted Beckmann problem with boundary costs ⋮ Optimal controlled transports with free end times subject to import/export tariffs ⋮ An optimal-transport finite-particle method for mass diffusion ⋮ Optimal Transport Approach to Sobolev Regularity of Solutions to the Weighted Least Gradient Problem ⋮ Sharp semi-concavity in a non-autonomous control problem and \(L^p\) estimates in an optimal-exit MFG ⋮ Optimal free export/import regions

Cites Work

• Absolute continuity and summability of transport densities: simpler proofs and new estimates
• Convex analysis and measurable multifunctions
• Regularity properties for Monge transport density and for solutions of some shape optimization problem
• Representation of equilibrium solutions to the table problem for growing sandpiles
• Uniqueness and transport density in Monge's mass transportation problem
• Optimal transport for applied mathematicians. Calculus of variations, PDEs, and modeling
• An optimal transportation problem with a cost given by the Euclidean distance plus import/export taxes on the boundary
• On a dual formulation for the growing sandpile problem
• Summability estimates on transport densities with Dirichlet regions on the boundaryviasymmetrization techniques
• INTEGRAL ESTIMATES FOR TRANSPORT DENSITIES
• Sharp summability for Monge Transport densityviaInterpolation
• Characterization of optimal shapes and masses through Monge-Kantorovich equation
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