Nondegeneracy of the bubble in the critical case for nonlocal equations

By J. D'avila, Manuel del Pino, Yannick Sire. 2013

94 citations recorded by the source corpus.

We prove the nondegeneracy of the extremals of the fractional Sobolev inequality as solutions of a critical semilinear nonlocal equation involving the fractional Laplacian.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/48fd32529b40f3f786fae16698dd1bd67a9c11e7

Citations in the corpus

• ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR NONLINEAR ELLIPTIC PROBLEMS WITH THE FRACTIONAL LAPLACIAN (2013, unknown): “LC = ∂Ω×(0,∞), ∂s νU= Up +ǫU on Ω×{0}, (5.1) where 0 <s<1 and p= n+2s n−2s. We remind that the functions wλ,ξ and Wλ,ξ are defined in (2.5) and (2.8). By the result of D´avila, del Pino and Sire [14], it is known that the space of the bounded solutions for the linearized equation of (2.7) at wλ”