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1Department of Mathematics and Statistics, University of Alaska Fairbanks, Fairbanks, AK 99775-6660, USA. Email: ffsaa@uaf.edu
2Department of Mathematics, University of Linköping, Linköping, Sweden. Email: vlkoz@mai.liu.se
3Department of Mathematics and Statistics, University of Alaska Fairbanks, Fairbanks, AK 99775-6660, USA. Email: david.maxwell@uaf.edu
4Department of Physics and Geophysical Institute, University of Alaska Fairbanks, Fairbanks, AK 99775, USA. Email: truffer@gi.alaska.edu
Citation Information: Journal of Inverse and Ill-posed Problems. Volume 17, Issue 3, Pages 239–258, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: 10.1515/JIIP.2009.018, April 2009
We address a Cauchy problem for a nonlinear elliptic PDE arising in glaciology. After recasting the Cauchy problem as an ill-posed operator equation, we prove (for values of a certain parameter allowing Hilbert space techniques) differentiability properties of the associated operator. We also suggest iterative methods which can be applied to solve the operator problem.
Key words.: Inverse boundary problems; nonlinear elliptic equations; iterative methods
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