Analysis Seminar

Uniqueness and Nondegeneracy of Ground States for Non-Local Equations

We consider the non-local and non-linear equation (Δ)sQ+QQα+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-101

Speakers

Rupert Frank

Affiliation

Princeton University

Event Series

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