ON THE MINIMUM OF CONTINUOUS FUNCTIONALS OF DERIVATIVES FOR A HARMONIC FUNCTION PARAMETRIZED BY ITS DESIRED LEVEL LINE AND/OR OTHER BOUNDARY DATA

摘要

The author shows the possibility (partially noted in [4] and [5]) of applying of the Helmholtz-Kirchhoff method both to the proof of the existence and to the numerical search for the minimum of certain lower continuous functionals (including nondifferentiable ones) depending on derivatives of a harmonic function parametrized by its desired level line and/or other boundary data. One of the problems considered was posed in [9] by A. A. Sozykin, a researcher of the Tupolev Aviation Science and Technology Complex. It is connected with the problem of icing of elements of the bodies of flying vehicles. The other problem is connected with the problem of estimating the efficiency of turbines in an open flow (see [13-17]). Possible generalizations are outlined.