ELLIPTIC EQUATIONS WITH DIFFUSION COEFFICIENT VANISHING AT THE BOUNDARY: THEORETICAL AND COMPUTATIONAL ASPECTS

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...

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Bibliographic Details
Published in:Quarterly of applied mathematics 2006-12, Vol.64 (4), p.735-747
Main Authors: LEE, CHUNG-MIN, RUBINSTEIN, JACOB
Format: Article
Language:English
Subjects:
Applied mathematics
Boundary conditions
Coefficients
Diffusion coefficient
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Geometric planes
Mathematical constants
Mathematical functions
Optics
Physics
Sensors
Spectral methods
Uniqueness
Wave optics
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Summary: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.
ISSN:0033-569X
1552-4485
DOI:10.1090/S0033-569X-06-01033-1