ABSTRACT
In [1,2], it is shown that the problem (Pp) admits a unique solution up. It is also interesting to mention that for p = 1, the problem splits into two separate problems, namely two thin-plate spline problems (of order 2), one for each of the components u\ and u2. On the contrary, for p φ 1, the problem is effectively coupled in the two components. The coefficient p allows to control the relative magnitude of the two terms of the functional. Moreover, when p —► 0 and p —► -f oo, the solution up tends towards finite limits.
