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

D. Maxwell, Conformal parameterizations of Kasner spacetimes, preprint, 2014

D. Maxwell, The conformal method and the conformalthin sandwich methods are the same, preprint, 2014
(arxiv:1402.5585)

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)

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)

D. Maxwell, Rough solutions of the Einstein constraint equations,
J. Reine Ang. Math., 590 (2006), 1  30
(grqc/0405088)

D. Maxwell, Solutions of the Einstein constraint equations with apparent horizon boundaries, Comm. Math. Phys. 256 (2005), 561  583.
(grqc/0307117)

D. Maxwell, Rough solutions of the Einstein constraint equations on compact manifolds, J. Hyp. Diff. Eq. 2 (2005), 521  546.
(grqc/0506085)

J. Isenberg, D. Maxwell, D. Pollack, A gluing construction for nonvacuum solutions of the Einstein constraint equations, to appear Adv. Theor. Math. Phys., (2005).
(grqc/0501083)

D. Maxwell, Initial Data for Black Holes and Rough Spacetimes, Dissertation,
University of Washington, 2004 (PDF)
Inverse problems in glaciology

M. Habermann, M. Truffer, and D. Maxwell, Changing basal conditions during the speedup of Jakobshavn IsbrÃ¦, Greenland, The Cryosphere, vol. 7, no. 6, pp. 1679—1692, 2013

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, KozlovMaz'ya iteration as a form of Landweber iteration, (to appear: Inverse Problems and Imaging)

D. Maxwell, M. Truffer, and S. Avdonin,
Inverse Methods for Reconstructing Basal Boundary Data
Poster, AGU Fall Meeting, 2008.

D. Maxwell, M. Truffer, S. Avdonin, and M. Steuffer,
An iterative scheme for determining glacier velocities and stresses,
J. Glac., 54 (2008), 888—898.

S. Avdonin, V. Kozlov, D. Maxwell, and M. Truffer. Iterative methods for solving a nonlinear
boundary inverse problem in glaciology, J. Inverse IllPosed Problems, 2008.
NonNewtonian fluid flow

D. Maxwell, A regularity technique for nonlinear Stokeslike elliptic
systems,
NavierStokes Equations and Related Nonlinear Problems
(H. Amann, G.P. Galdi, K. Pileckas and V.A. Solonnikov eds.),
VSP, 1998, pp. 165181.

D. Maxwell, On the regularity of a model nonNewtonian fluid, MSc Thesis,
University of British Columbia, 1997 (PDF)