A Faber-Krahn inequality for mixed local and nonlocal operators

By Stefano Biagi, Serena Dipierro, Enrico Valdinoci, E. Vecchi. Journal d'Analyse Mathematique, 2021

82 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2e13487188e7ff158bdea7a9b50cdc1bf7dafa4b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. P. Garain
2. Vicentiu D. Rădulescu
3. A. Ukhlov
4. R. Arora
5. Erik Lindgren
6. Jiwen Zhang
7. Xifeng Su
8. Yuanhong Wei

In Computational Theory and Mathematics

1. Vicentiu D. Rădulescu
2. P. Garain
3. R. Arora
4. A. Ukhlov
5. Erik Lindgren
6. Enrico Valdinoci
7. Binlin Zhang
8. Mingqi Xiang

In Mathematical Physics

1. P. Garain
2. Vicentiu D. Rădulescu
3. A. Ukhlov
4. Erik Lindgren
5. R. Arora
6. Jiwen Zhang
7. Xifeng Su
8. Yuanhong Wei

Citations in the corpus

• Combined effects in mixed local–nonlocal stationary problems (2021, background): “Some questions related to structural results like existence, maximum principle and interior Sobolev and Lipschitz regularity [1, 11, 14], symmetry results [13], Faber-Krahn type inequality [12], Neumann problems [42], Green functions estimates [26, 27] has been answered.”
• Mixed local and nonlocal Sobolev inequalities with extremal and associated quasilinear singular elliptic problems (2021, background): “For related results, see also da Silva-Salort [29], Biagi-Dipierro-ValdinociVecchi [14] and the references therein.”
• Higher Hölder regularity for mixed local and nonlocal degenerate elliptic equations (2022, methodology): “We also refer to Biagi-Dipierro-Valdinoci-Vecchi [4, 8], Dipierro-RosOton-Serra-Valdinoci [22], Dipierro-Proietti Lippi-Valdinoci [21], Dipierro-Valdinoci [23] and the references therein.”
• Regularity results for solutions of mixed local and nonlocal elliptic equations (2022, background): “Moreover, mixed operators have recently received a great attention from different points of view, including regularity theory [2, 3, 8, 10, 12, 14, 15, 17, 25], existence and non-existence results [1, 6, 28], eigenvalue problems [13, 16, 22], shape optimization and calculus of variations [7, 11], sy”