Data di Pubblicazione:
2015
Citazione:
Concentration phenomena for the nonlocal Schrödinger equation with Dirichlet datum / J. Dávila, M. Del Pino, S. Dipierro, E. Valdinoci. - In: ANALYSIS & PDE. - ISSN 2157-5045. - 8:5(2015), pp. 1165-1235.
Abstract:
For a smooth, bounded domain Ω, s ∈ (0, 1), p ∈ (1, (n+2s)/(n-2s)) we consider the nonlocal equation ε2s(-Δ)su+u = up in Ω with zero Dirichlet datum and a small parameter ε > 0. We construct a family of solutions that concentrate as ε → 0 at an interior point of the domain in the form of a scaling of the ground state in entire space. Unlike the classical case s = 1, the leading order of the associated reduced energy functional in a variational reduction procedure is of polynomial instead of exponential order on the distance from the boundary, due to the nonlocal effect. Delicate analysis is needed to overcome the lack of localization, in particular establishing the rather unexpected asymptotics for the Green function of ε2s(-Δ)s+1 in the expanding domain ε-1Ω with zero exterior datum.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Concentration phenomena; Green functions; Nonlocal quantum mechanics; Analysis; Applied Mathematics; Numerical Analysis
Elenco autori:
J. Dávila, M. Del Pino, S. Dipierro, E. Valdinoci
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