Artículo

Dávila, J.; López Ríos, L.; Sire, Y."Bubbling solutions for nonlocal elliptic problems" (2017) Revista Matematica Iberoamericana. 33(2):509-546
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Abstract:

We investigate bubbling solutions for the nonlocal equation Aω s u = up, u > 0 in ω, under homogeneous Dirichlet conditions, where ω is a bounded and smooth domain. The operator As ω stands for two types of nonlocal operators that we treat in a unified way: either the spectral fractional Laplacian or the restricted fractional Laplacian. In both cases s ∈ (0, 1), and the Dirichlet conditions are different: for the spectral fractional Laplacian, we prescribe u = 0 on ∂ω, and for the restricted fractional Laplacian, we prescribe u = 0 on ℝn\\ω. We construct solutions when the exponent p = (n+2s)/(n-2s)±ϵ is close to the critical one, concentrating as ϵ → 0 near critical points of a reduced function involving the Green and Robin functions of the domain. © European Mathematical Society.

Registro:

Documento: Artículo
Título:Bubbling solutions for nonlocal elliptic problems
Autor:Dávila, J.; López Ríos, L.; Sire, Y.
Filiación:Departamento de Ingeniería Matemática and CMM, Universidad de Chile, Casilla 170 Correo 3, Santiago, Chile
Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, 1428, Argentina
Institut de Mathématiques de Marseille, Université D'Aix-Marseille, 9 rue F. Joliot Curie, Marseille Cedex 13, 13453, France
Palabras clave:Dirichlet problem; Fractional Laplacian; Stable critical points; Sub and supercritical exponents
Año:2017
Volumen:33
Número:2
Página de inicio:509
Página de fin:546
DOI: http://dx.doi.org/10.4171/rmi/947
Handle:http://hdl.handle.net/20.500.12110/paper_02132230_v33_n2_p509_Davila
Título revista:Revista Matematica Iberoamericana
Título revista abreviado:Rev. Mat. Iberoam.
ISSN:02132230
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02132230_v33_n2_p509_Davila

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Citas:

---------- APA ----------
Dávila, J., López Ríos, L. & Sire, Y. (2017) . Bubbling solutions for nonlocal elliptic problems. Revista Matematica Iberoamericana, 33(2), 509-546.
http://dx.doi.org/10.4171/rmi/947
---------- CHICAGO ----------
Dávila, J., López Ríos, L., Sire, Y. "Bubbling solutions for nonlocal elliptic problems" . Revista Matematica Iberoamericana 33, no. 2 (2017) : 509-546.
http://dx.doi.org/10.4171/rmi/947
---------- MLA ----------
Dávila, J., López Ríos, L., Sire, Y. "Bubbling solutions for nonlocal elliptic problems" . Revista Matematica Iberoamericana, vol. 33, no. 2, 2017, pp. 509-546.
http://dx.doi.org/10.4171/rmi/947
---------- VANCOUVER ----------
Dávila, J., López Ríos, L., Sire, Y. Bubbling solutions for nonlocal elliptic problems. Rev. Mat. Iberoam. 2017;33(2):509-546.
http://dx.doi.org/10.4171/rmi/947