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arXiv · 2501.05320

Isoperimetric inequalities for the fractional composite membrane problem

Mrityunjoy Ghosh
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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.

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Mrityunjoy Ghosh. 2025-01-09. Isoperimetric inequalities for the fractional composite membrane problem. https://doi.org/10.1007/s00013-024-02090-x

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