Some recent work involves inverse problems in glaciology.
- D. Maxwell, Kozlov-Maz'ya iteration as a form of Landweber iteration, (in prep.)
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D. Maxwell, M. Truffer, S. Avdonin,
Inverse Methods for Reconstructing Basal Boundary Data
Poster, AGU Fall Meeting, 2008.
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D. Maxwell, M. Truffer, S. Avdonin, 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.
Ongoing work concerning the Einstein constraint equations; these form an elliptic-like system
of equations that arises in general relativity.
Many of the items below can be found in the gr-qc section of
the arxiv.
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D. Maxwell, A model problem for conformal parameterizations of the Einstein constraint equations,
to appear, Comm. Math. Phys. (2010) (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)
Earlier in life, I studied non-Newtonian versions of the Navier-Stokes
equations.
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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)