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• W1551806580 abstract "We establish existence and qualitative properties of saddle-shaped solutions of the elliptic fractional equation (−∆)u = f(u) in all the space R, where f is of bistable type. These solutions are odd with respect to the Simons cone and even with respect to each coordinate. More precisely, we prove the existence of a saddle-shaped solution in every even dimension 2m, as well as its monotonicity properties, asymptotic behaviour, and instability in dimensions 2m = 4 and 2m = 6. These results are relevant in connection with the analog for fractional equations of a conjecture of De Giorgi on the 1-D symmetry of certain solutions. Saddleshaped solutions are the simplest candidates, besides 1-D solutions, to be global minimizers in high dimensions, a property not yet established." @default.
• W1551806580 created "2016-06-24" @default.
• W1551806580 creator A5023275575 @default.
• W1551806580 date "2013-09-24" @default.
• W1551806580 modified "2023-09-24" @default.
• W1551806580 title "Saddle-shaped solutions of bistable elliptic equations involving the half-Laplacian" @default.
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• W1551806580 doi "https://doi.org/10.2422/2036-2145.201107_002" @default.
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