Analytic monotone extension of boundary data
We derive several schemes that extend a monotone function on the boundary of the unit square to be a monotone function on the unit square while maintaining the smoothness of the function. Our results are related to those of Dahmen, DeVore, and Micchelli and have application to the modeling of charge distribution in semi-conductor design.
Sun, X. P., and X. M. Yu. "Analytic monotone extension of boundary data." Journal of Approximation Theory 77, no. 3 (1994): 314-330.
Journal of Approximation Theory