Abstract
We consider the first Dirichlet eigenvalue problem for a mixed local/nonlocal elliptic operator and we establish a quantitative Faber-Krahn inequality. More precisely, we show that balls minimize the first eigenvalue among sets of given volume and we provide a stability result for sets that almost attain the minimum.
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Acknowledgments
We would like to thank Professor Lorenzo Brasco for pointing to our attention the paper [2] and for some interesting and pleasant discussions.
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The authors are members of INdAM. S. Biagi is partially supported by the INdAM-GNAMPA project Metodi topologici per problemi al contorno associati a certe classi di equazioni alle derivate parziali. S. Dipierro and E. Valdinoci are members of AustMS. S. Dipierro is supported by the Australian Research Council DECRA DE180100957 “PDEs, free boundaries and applications”. E. Valdinoci is supported by the Australian Laureate Fellowship FL190100081 “Minimal surfaces, free boundaries and partial differential equations”. E. Vecchi is partially supported by the INdAM-GNAMPA project Convergenze variazionali per funzionali e operatori dipendenti da campi vettoriali.
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Biagi, S., Dipierro, S., Valdinoci, E. et al. A Faber-Krahn inequality for mixed local and nonlocal operators. JAMA 150, 405–448 (2023). https://doi.org/10.1007/s11854-023-0272-5
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DOI: https://doi.org/10.1007/s11854-023-0272-5