О геометрической медиане выпуклых, а также треугольных и других многоугольных областей
The classical Fermat-Torricelli problem consists in finding the point which minimizes the sum of distances from it to the three vertices of a given triangle. The generalized Fermat-Torricelli problem concerns minimizing a weighted sum of distances, and it is one of the main problems in Facility Location theory. An analytic solution of Fermat-Torricelli problem is non-trivial even in the case of three points, and the general case is quite complex.
In this work we consider a further generalization, namely the continuous case in which we look for a geometric median of a two-dimensional domain, where the sum of distances is being replaced by an integral.