On the line with density |x|^p, we prove that the best single bubble is an interval with endpoint at the origin and that the best double bubble is two adjacent intervals that meet at the origin.
Huang, Juiyu; Qian, Xinkai; Pan, Yiheng; Xu, Mulei; Yang, Lu; and Zhou, Junfei
"Isoperimetric Problems on the Line with Density |𝑥|ᵖ,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 20:
2, Article 5.
Available at: https://scholar.rose-hulman.edu/rhumj/vol20/iss2/5