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Elliptic equations with diffusion coefficient vanishing at the boundary: Theoretical and computational aspects
Author(s):
Chung-min
Lee;
Jacob
Rubinstein
Journal:
Quart. Appl. Math.
64
(2006),
735-747.
MSC (2000):
Primary 35J70
Posted:
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
PII:
S0033-569X-06-01033-1
Received by editor(s):
March 13, 2006
Posted:
November 8, 2006
Copyright of article:
Copyright
2006,
Brown University
The copyright for this article reverts to public domain after 28 years from publication.
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