Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Elliptic equations with diffusion coefficient vanishing at the boundary: Theoretical and computational aspects

Authors: Chung-min Lee and Jacob Rubinstein
Journal: Quart. Appl. Math. 64 (2006), 735-747
MSC (2000): Primary 35J70
Published electronically: November 8, 2006
MathSciNet review: 2284468
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Abstract: A class of degenerate elliptic PDEs is considered. Specifically, it is assumed that the diffusion coefficient vanishes on the boundary of the domain. It is shown that if the diffusion coefficient vanishes fast enough, then the problem has a unique solution in the class of smooth functions even if no boundary conditions are supplied. A numerical method is derived to compute solutions for such degenerate equations. The problem is motivated by a certain approach to the recovery of the phase of a wave from intensity measurements.

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Additional Information

Chung-min Lee
Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
Email: chunglee@indiana.edu

Jacob Rubinstein
Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
Email: jrubinst@indiana.edu

DOI: https://doi.org/10.1090/S0033-569X-06-01033-1
Received by editor(s): March 13, 2006
Published electronically: November 8, 2006
Article copyright: © Copyright 2006 Brown University
The copyright for this article reverts to public domain 28 years after publication.

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