Published Paper

Inserted: 24 jan 2025
Last Updated: 24 jan 2025

Journal: Arch. Math. (Basel)
Year: 2025
Doi: 10.1007/s00013-024-02090-x

Abstract:

In this article, we investigate some isoperimetric-type inequalities related to the first eigenvalue of the fractional composite membrane problem. First, we establish an analogue of the renowned Faber-Krahn inequality for the fractional composite membrane problem. Next, we investigate an isoperimetric inequality for the first eigenvalue of the fractional composite membrane problem on the intersection of two domains-a problem that was first studied by Lieb 23 for the Laplacian. Similar results in the local case were previously obtained by Cupini-Vecchi 9 for the composite membrane problem. Our findings provide further insights into the fractional setting, offering a new perspective on these classical inequalities.