Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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


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
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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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Additional Information

Michael Westdickenberg
Affiliation: Lehrstuhl für Mathematik (Analysis), RWTH Aachen University, Templergraben 55, 52062 Aachen, Germany
Email: mwest@instmath.rwth-aachen.de

DOI: https://doi.org/10.1090/qam/1459
Keywords: Compressible gas dynamics, optimal transport
Received by editor(s): March 16, 2016
Received by editor(s) in revised form: October 14, 2016
Published electronically: November 14, 2016
Article copyright: © Copyright 2016 Brown University


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