Smoothest Interpolation in the Mean

Smoothest interpolation with boundary conditions in $W^3_2[a,b]$

“…Various modifications of the problem have been studied by Bojanov [4], Draganova in [7] for the periodic case and on interpolation in mean values in [8]. Multidimensional aspects of the problem (1.1) have been considered by Marin [10], Rademacher and Scherer [14], Scherer and Smith [16], Scherer [15].…”