Some results on the eigenvalue problem for a fractional elliptic equation

Abstract

Abstract This paper deals with the eigenvalue problem for a fractional variable coefficients elliptic equation defined on a bounded domain. Compared to the previous work, we prove a quite different variational formulation of the first eigenvalue for the above problem. This allows us to give a variational proof of the fractional Faber–Krahn inequality by employing suitable rearrangement techniques.

Keywords

• Eigenvalue
• Faber–Krahn inequality
• Rearrangement