Example of minimizer of the average-distance problem with non closed set of corners
Xin Yang LuCarnegie Mellon University, Pittsburgh, USA
The average-distance problem, in the penalized formulation, involves minimizing
among compact, connected sets , where denotes the 1-Hausdorff measure, , is a given measure and a given parameter. Regularity of minimizers is a delicate problem. It is known that even if is absolutely continuous with respect to Lebesgue measure, regularity does not hold in general. An interesting question is whether the set of corners, i.e. points where regularity does not hold, is closed. The aim of this paper is to provide an example of minimizer whose set of corners is not closed, with reference measure absolutely continuous with respect to Lebesgue measure.
Cite this article
Xin Yang Lu, Example of minimizer of the average-distance problem with non closed set of corners. Rend. Sem. Mat. Univ. Padova 137 (2017), pp. 19–55DOI 10.4171/RSMUP/137-2