Symmetry breaking for an elliptic equation involving the Fractional Laplacian

Abstract

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.

19 pages. Some minor corrections and improvements

References in corpus (3)

• Existence and symmetry results for a Schrödinger type problem involving the fractional Laplacian
• Radial symmetry of positive solutions involving the fractional Laplacian
• Convexity Properties of Dirichlet Integrals and Picone-type Inequalities

Cited by in corpus (1)

• Symmetry breaking for Schrödinger-Poisson-Slater energy