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June 2003 Generalized Snell's Law for Weighted Minimal Surface in Heterogeneous Media
Zhilin Li, Xiaobiao Lin, Monica Torres, Hongkai Zhao
Methods Appl. Anal. 10(2): 199-214 (June 2003).


The weighted minimal surface problem in heterogeneous media is studied in this paper. The solution to the weighted minimal surface problem is continuous but the derivatives have a jump across the interface where the medium property is discontinuous. The jump condition of the derivatives derived in this paper generalized the Snell's law in geometric optics to weighted minimal surfaces of co-dimension one in any dimensional space. A numerical method based on the gradient flow and the maximum principal preserving immersed interface method is developed to solve this nonlinear elliptic interface problem with jump conditions. Numerical computations are presented to verify both the analysis and the numerical algorithm.


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Zhilin Li. Xiaobiao Lin. Monica Torres. Hongkai Zhao. "Generalized Snell's Law for Weighted Minimal Surface in Heterogeneous Media." Methods Appl. Anal. 10 (2) 199 - 214, June 2003.


Published: June 2003
First available in Project Euclid: 17 June 2005

zbMATH: 1081.35034
MathSciNet: MR2074748

Rights: Copyright © 2003 International Press of Boston

Vol.10 • No. 2 • June 2003
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