Methods and Applications of Analysis

Generalized Snell's Law for Weighted Minimal Surface in Heterogeneous Media

Zhilin Li, Xiaobiao Lin, Monica Torres, and Hongkai Zhao


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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Methods Appl. Anal., Volume 10, Number 2 (2003), 199-214.

First available in Project Euclid: 17 June 2005

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Li, Zhilin; Lin, Xiaobiao; Torres, Monica; Zhao, Hongkai. Generalized Snell's Law for Weighted Minimal Surface in Heterogeneous Media. Methods Appl. Anal. 10 (2003), no. 2, 199--214.

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