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.
Bulanyi, B. (2021). On the importance of the connectedness assumption in the statement of the optimal p-compliance problem. Journal of Mathematical Analysis and Applications, 499(2), np. https://doi.org/10.1016/j.jmaa.2021.125064 (Original work published 2021)