My research has focused on:
- The construction of slices of spacetime in General Relativity.
- Inverse problems in glaciology.
These seem like bizarrely unrelated topics, but both apply partial differential equations at the
boundary between mathematics and physics.
Slices of spacetime
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D. Maxwell, Conformal parameterizations of Kasner spacetimes, preprint, 2014
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D. Maxwell, The conformal method and the conformal-thin sandwich methods are the same, preprint, 2014
(arxiv:1402.5585)
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D. Maxwell, A model problem for conformal parameterizations of the Einstein constraint equations,
Comm. Math. Phys., vol. 302, no. 3, pp. 697—736, 2011.
(arxiv:0909.5674)
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D. Maxwell, A class of solutions of the vacuum Einstein constraint equations with freely specified
mean curvature,
Math. Res. Lett. 16 (2009), no. 4, 627 - 645.
(arXiv:0804.0874)
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D. Maxwell, Rough solutions of the Einstein constraint equations,
J. Reine Ang. Math., 590 (2006), 1 - 30
(gr-qc/0405088)
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D. Maxwell, Solutions of the Einstein constraint equations with apparent horizon boundaries, Comm. Math. Phys. 256 (2005), 561 - 583.
(gr-qc/0307117)
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D. Maxwell, Rough solutions of the Einstein constraint equations on compact manifolds, J. Hyp. Diff. Eq. 2 (2005), 521 - 546.
(gr-qc/0506085)
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J. Isenberg, D. Maxwell, D. Pollack, A gluing construction for non-vacuum solutions of the Einstein constraint equations, to appear Adv. Theor. Math. Phys., (2005).
(gr-qc/0501083)
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D. Maxwell, Initial Data for Black Holes and Rough Spacetimes, Dissertation,
University of Washington, 2004 (PDF)
Inverse problems in glaciology
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M. Habermann, M. Truffer, and D. Maxwell, Changing basal conditions during the speed-up of Jakobshavn Isbræ, Greenland, The Cryosphere, vol. 7, no. 6, pp. 1679—1692, 2013
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M. Habermann, D. Maxwell, and M. Truffer, Reconstruction of basal properties in ice sheets using iterative inverse methods, Journal of Glaciology, vol. 58, pp. 795—807, 2012
- D. Maxwell, Kozlov-Maz'ya iteration as a form of Landweber iteration, (to appear: Inverse Problems and Imaging)
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D. Maxwell, M. Truffer, and S. Avdonin,
Inverse Methods for Reconstructing Basal Boundary Data
Poster, AGU Fall Meeting, 2008.
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D. Maxwell, M. Truffer, S. Avdonin, and M. Steuffer,
An iterative scheme for determining glacier velocities and stresses,
J. Glac., 54 (2008), 888—898.
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S. Avdonin, V. Kozlov, D. Maxwell, and M. Truffer. Iterative methods for solving a nonlinear
boundary inverse problem in glaciology, J. Inverse Ill-Posed Problems, 2008.
Non-Newtonian fluid flow
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D. Maxwell, A regularity technique for nonlinear Stokes-like elliptic
systems,
Navier-Stokes Equations and Related Nonlinear Problems
(H. Amann, G.P. Galdi, K. Pileckas and V.A. Solonnikov eds.),
VSP, 1998, pp. 165-181.
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D. Maxwell, On the regularity of a model non-Newtonian fluid, MSc Thesis,
University of British Columbia, 1997 (PDF)