Generalized Snell's Law for Weighted Minimal Surface in Heterogeneous Media
Li, Zhilin ; Lin, Xiaobiao ; Torres, Monica ; Zhao, Hongkai
Methods Appl. Anal., Tome 10 (2003) no. 3, p. 199-214 / Harvested from Project Euclid
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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.
Publié le : 2003-06-14
Classification:  
@article{1119018753,
     author = {Li, Zhilin and Lin, Xiaobiao and Torres, Monica and Zhao, Hongkai},
     title = {Generalized Snell's Law for Weighted Minimal Surface in
Heterogeneous Media},
     journal = {Methods Appl. Anal.},
     volume = {10},
     number = {3},
     year = {2003},
     pages = { 199-214},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1119018753}
}

Li, Zhilin; Lin, Xiaobiao; Torres, Monica; Zhao, Hongkai. Generalized Snell's Law for Weighted Minimal Surface in
Heterogeneous Media. Methods Appl. Anal., Tome 10 (2003) no. 3, pp.  199-214. http://gdmltest.u-ga.fr/item/1119018753/