
Analysis Seminar
Uniqueness and Nondegeneracy of Ground States for Non-Local Equations
We consider the non-local and non-linear equation (−Δ)sQ+Q−Qα+1=0 involving the fractional Laplacian (−Δ)s with 0<s<1. We prove uniqueness of energy minimizing solutions for the optimal range of α's. As a technical key result, we show that the associated linearized operator is nondegenerate, in the sense that its kernel is spanned by ∇Q. This solves an open problem posed by Weinstein and by Kenig, Martel and Robbiano.
The talk is based on joint work with E. Lenzmann and L. Sylvestre.
Date & Time
October 19, 2012 | 3:15pm – 4:15pm
Location
S-101Speakers
Rupert Frank
Affiliation
Princeton University