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.
Geometric inequalities for fractional Laplace operators and Applications / Cinti, Eleonora; Ferrari, Fausto. - In: NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS. - ISSN 1021-9722. - STAMPA. - 22:6(2015), pp. 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.