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Gamma convergence of an energy functional related to the fractional Laplacian

Author
Gonzalez, M.
Type of activity
Journal article
Journal
Calculus of variations and partial differential equations
Date of publication
2009
Volume
36
Number
2
First page
173
Last page
210
Repository
http://hdl.handle.net/2117/7883 Open in new window
Abstract
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...
Citation
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.
Group of research
EDP - Partial Differential Equations and Applications

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