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Gamma convergence of an energy functional related to the fractional Laplacian

Autor
Gonzalez, M.
Tipus d'activitat
Article en revista
Revista
Calculus of variations and partial differential equations
Data de publicació
2009
Volum
36
Número
2
Pàgina inicial
173
Pàgina final
210
Repositori
http://hdl.handle.net/2117/7883 Obrir en finestra nova
Resum
We prove a Γ -convergence result for an energy functional related to some fractional powers of the Laplacian operator, (−Δ)s for 1/2 < s < 1, with two singular perturbations, that leads to a two-phase problem. The case (−Δ)1/2 was considered by Alberti–Bouchitté–Seppecher in relation to a model in capillarity with line tension effect. However, the proof in our setting requires some new ingredients such as the Caffarelli–Silvestre extension for the fractional Laplacian and new trace...
Citació
González, M. Gamma convergence of an energy functional related to the fractional Laplacian. "Calculus of variations and partial differential equations", 2009, vol. 36, núm. 2, p. 173-210.
Grup de recerca
EDP - Equacions en Derivades Parcials i Aplicacions

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