My research has focused on:
These seem like bizarrely unrelated topics, but both apply partial differential equations at the
boundary between mathematics and physics.
- The construction of slices of spacetime in General Relativity.
- Inverse problems in glaciology.
Slices of spacetime
D. Maxwell, Conformal parameterizations of Kasner spacetimes, preprint, 2014
D. Maxwell, The conformal method and the conformal-thin sandwich methods are the same, preprint, 2014
D. Maxwell, A model problem for conformal parameterizations of the Einstein constraint equations,
Comm. Math. Phys., vol. 302, no. 3, pp. 697—736, 2011.
D. Maxwell, A class of solutions of the vacuum Einstein constraint equations with freely specified
Math. Res. Lett. 16 (2009), no. 4, 627 - 645.
D. Maxwell, Rough solutions of the Einstein constraint equations,
J. Reine Ang. Math., 590 (2006), 1 - 30
D. Maxwell, Solutions of the Einstein constraint equations with apparent horizon boundaries, Comm. Math. Phys. 256 (2005), 561 - 583.
D. Maxwell, Rough solutions of the Einstein constraint equations on compact manifolds, J. Hyp. Diff. Eq. 2 (2005), 521 - 546.
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).
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 speed-up of Jakobshavn Isbræ, 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, Kozlov-Maz'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 Ill-Posed Problems, 2008.
Non-Newtonian fluid flow
D. Maxwell, A regularity technique for nonlinear Stokes-like elliptic
Navier-Stokes Equations and Related Nonlinear Problems
(H. Amann, G.P. Galdi, K. Pileckas and V.A. Solonnikov eds.),
VSP, 1998, pp. 165-181.
D. Maxwell, On the regularity of a model non-Newtonian fluid, MSc Thesis,
University of British Columbia, 1997 (PDF)