Symmetry breaking for an elliptic equation involving the Fractional   Laplacian
  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. De N\'apoli
math.AP math.FA