Leonori, TommasoMedina, MariaPeral, IreneoPrimo, AnaSoria, Fernando2024-11-202024-11-202018-07-15Tommaso Leonori, Maria Medina, Ireneo Peral, Ana Primo, Fernando Soria, Principal eigenvalue of mixed problem for the fractional Laplacian: Moving the boundary conditions, Journal of Differential Equations, Volume 265, Issue 2, 2018, Pages 593-619, ISSN 0022-0396, https://doi.org/10.1016/j.jde.2018.03.0010022-0396https://doi.org/10.1016/j.jde.2018.03.001https://hdl.handle.net/20.500.14468/24442We analyze the behavior of the eigenvalues of the following nonlocal mixed problem {(−Δ)su=λ1(D)u in Ω,u=0 in D,Nsu=0 in N. Our goal is to construct different sequences of problems by modifying the configuration of the sets D and N, and to provide sufficient and necessary conditions on the size and the location of these sets in order to obtain sequences of eigenvalues that in the limit recover the eigenvalues of the Dirichlet or Neumann problem. We will see that the nonlocality plays a crucial role here, since the sets D and N can have infinite measure, a phenomenon that does not appear in the local case (see for example [6–8]).eninfo:eu-repo/semantics/openAccess12 MatemáticasartículoMixed problemsFractional LaplacianEigenvalues