Accepted Paper

Inserted: 2 sep 2015
Last Updated: 2 sep 2015

Journal: NoDea
Year: 2015

Abstract:

We prove a weighted fractional inequality involving the solution $u$ of a nonlocal semilinear problem in $\mathbb R^n$. Such inequality bounds a weighted $L^2$-norm of a compactly supported function $\phi$ by a weighted $H^s$-norm of $\phi$. 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.

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