We study the symmetry breaking phenomenon for an elliptic equation involving the fractional Laplacian in a large ball. Our main tool is an extension of the Strauss radial lemma involving the fractional Laplacian, which might be of independent interest; and from which we derive compact embedding theorems for a Sobolev-type space of radial functions with power weights.
Pablo L. Nápoli. "Symmetry breaking for an elliptic equation involving the Fractional Laplacian." Differential Integral Equations 31 (1/2) 75 - 94, January/February 2018. https://doi.org/10.57262/die/1509041402