A Global Compactness type result for Palais-Smale sequences in fractional Sobolev spaces

Abstract

We extend the Global Compactness result by M. Struwe (Math. Z, 1984) to any fractional Sobolev spaces ${\dot{H}}^s(\Omega )$ for $0<s<N/2$ and $\Omega \subset {\mathbb{R}}^N$ a bounded domain with smooth boundary. The proof is a simple direct consequence of the so-called Profile Decomposition of P. Gerard (ESAIM: Control, Optimisation and Calculus of Variations, 1998).

To appear in Nonlinear Analysis: Theory, Methods & Applications