In:
Bulletin of the Australian Mathematical Society, Cambridge University Press (CUP), Vol. 108, No. 2 ( 2023-10), p. 290-297
Abstract:
We extend a result of Lieb [‘On the lowest eigenvalue of the Laplacian for the intersection of two domains’, Invent. Math. 74 (3) (1983), 441–448] to the fractional setting. We prove that if A and B are two bounded domains in $\mathbb R^N$ and $\lambda _s(A)$ , $\lambda _s(B)$ are the lowest eigenvalues of $(-\Delta )^s$ , $0〈s〈1$ , with Dirichlet boundary conditions, there exists some translation $B_x$ of B such that $\lambda _s(A\cap B_x)〈 \lambda _s(A)+\lambda _s(B)$ . Moreover, without the boundedness assumption on A and B , we show that for any $\varepsilon〉0$ , there exists some translation $B_x$ of B such that $\lambda _s(A\cap B_x)〈 \lambda _s(A)+\lambda _s(B)+\varepsilon .$
Type of Medium:
Online Resource
ISSN:
0004-9727
,
1755-1633
DOI:
10.1017/S0004972722001356
Language:
English
Publisher:
Cambridge University Press (CUP)
Publication Date:
2023
detail.hit.zdb_id:
2268688-5
SSG:
17,1
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