A Liouville theorem for non local elliptic equations

Details A Liouville theorem for non local elliptic equations A Liouville theorem for non local elliptic equations

2009-09-09

arxiv.org/abs/0909.1650v1

Mathematics

Analysis of PDEs

Scientific paper

We prove a Liouville-type theorem for bounded stable solutions $v \in
C^2(\R^n)$ of elliptic equations of the type (-\Delta)^s v= f(v)\qquad {in
$\R^n$,} where $s \in (0,1)$ {and $f$ is any nonnegative function}. The
operator $(-\Delta)^s$ stands for the fractional Laplacian, a
pseudo-differential operator of symbol $|\xi |^{2s}$.

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