# On the importance of the connectedness assumption in the statement of the optimal $p$-compliance problem

created by bulanyi on 12 Jan 2021
modified on 12 Apr 2021

[BibTeX]

Published Paper

Inserted: 12 jan 2021
Last Updated: 12 apr 2021

Journal: Journal of Mathematical Analysis and Applications
Volume: 499
Number: 2
Pages: 9
Year: 2021
Doi: https://doi.org/10.1016/j.jmaa.2021.125064

ArXiv: 2101.04678 PDF

Abstract:

In this short note we provide a proof of the importance of the connectedness assumption in the statement of the optimal $p$-compliance problem with length penalization and in the statement of the constrained form of this problem for the existence of solutions.