Calculus of Variations and Geometric Measure Theory

G. Palatucci - A. Pisante

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

created by palatucci on 14 Jun 2014
modified on 18 Dec 2015


Published Paper

Inserted: 14 jun 2014
Last Updated: 18 dec 2015

Journal: Nonlinear Anal.
Volume: 117
Pages: 1-7
Year: 2015
Doi: doi:10.1016/


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).