The Stefan problem and free targets of optimal Brownian martingale transport

Martingales with discrete parameter (60G42) Stopping times; optimal stopping problems; gambling theory (60G40) PDEs with randomness, stochastic partial differential equations (35R60) Free boundary problems for PDEs (35R35) Second-order parabolic equations (35K10) Optimal transportation (49Q22)

Cites Work

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On a problem of optimal transport under marginal martingale constraints
Model-independent bounds for option prices -- a mass transport approach
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The obstacle problem revisited
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From optimal stopping boundaries to Rost's reversed barriers and the Skorokhod embedding
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The supercooled Stefan problem in one dimension
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A solution to the Monge transport problem for Brownian martingales
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Optimal stopping of stochastic transport minimizing submartingale costs
A Two-Sided Contracting Stefan Problem
The Ill-Posed Hele-Shaw Model and The Stefan Problem for Supercooled Water
The Two-Sided Stefan Problem with a Spatially Dependent Latent Heat
Compactness of stopping times
Crowd motion and evolution PDEs under density constraints
Regularity of a free boundary in parabolic potential theory
Optimal Brownian Stopping When the Source and Target Are Radially Symmetric Distributions
An $L^1$ Penalty Method for General Obstacle Problems
Quasi-static evolution and congested crowd transport
The Existence of Probability Measures with Given Marginals
The Existence of Certain Stopping Times on Brownian Motion
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A general one-phase Stefan problem
Optimal Transport
$BV$ estimates in optimal transportation and applications
The singular set in the Stefan problem

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