Instability of spherical interfaces in a nonlinear free boundary problem

Abstract

Existence and stability of spherically symmetric stationary interfaces in a two-phase boundary problem are studied in ${\bf R}^{N}$ $(N \geq 2)$. We show that there exist two such solutions: a large ball and a small one. The linearized eigenvalue problem shows that the large ball is unstable with some fastest growing mode. We specify the mode precisely.