We prove a weighted fractional inequality involving the solution u of a nonlocal semilinear problem in Rn. Such inequality bounds a weighted L2-norm of a compactly supported function ϕ by a weighted Hs-norm of ϕ. In this inequality a geometric quantity related to the level sets of u will appear. As a consequence we derive some relations between the stability of u and the validity of fractional Hardy inequalities.
Cinti, E., Ferrari, F. (2015). Geometric inequalities for fractional Laplace operators and Applications. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 22(6), 1699-1714 [10.1007/s00030-015-0340-3].
Geometric inequalities for fractional Laplace operators and Applications
CINTI, ELEONORA;FERRARI, FAUSTO
2015
Abstract
We prove a weighted fractional inequality involving the solution u of a nonlocal semilinear problem in Rn. Such inequality bounds a weighted L2-norm of a compactly supported function ϕ by a weighted Hs-norm of ϕ. In this inequality a geometric quantity related to the level sets of u will appear. As a consequence we derive some relations between the stability of u and the validity of fractional Hardy inequalities.File in questo prodotto:
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