Abstract
Our goal in this Chapter is to exploit the link between the least gradient problem and the Monge-Kantorovich optimal transport problem presented in the previous Chapter in order to obtain regularity and stability results for the least gradient problem. We also use it to study the least gradient problem on our model non-simply-connected domain: an annulus. Let us stress that the proofs of the results in this Chapter rely very strongly on the use of optimal transport techniques and for most of them there is currently no proof without using them; in particular, their validity is limited to the two-dimensional case.
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Górny, W., Mazón, J.M. (2024). Applications of Optimal Transport Techniques. In: Functions of Least Gradient. Monographs in Mathematics, vol 110. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-51881-2_10
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DOI: https://doi.org/10.1007/978-3-031-51881-2_10
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-031-51880-5
Online ISBN: 978-3-031-51881-2
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