Euler-Lagrange equation for a minimization problem over monotone transport maps

Westdickenberg, Michael

doi:10.1090/qam/1459

Author: Michael Westdickenberg
Journal: Quart. Appl. Math. 75 (2017), 267-285
MSC (2010): Primary 35L65, 49J40, 82C40
DOI: https://doi.org/10.1090/qam/1459
Published electronically: November 14, 2016
MathSciNet review: 3614498
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Abstract: A variational time discretization for the compressible Euler equations has been introduced recently. It involves a minimization problem over the cone of monotone transport maps in each timestep. A matrix-valued measure field appears in the minimization as a Lagrange multiplier for the monotonicity constraint. We show that the absolutely continuous part of this measure field vanishes in the support of the density.

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