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

Giampiero Palatucci; Adriano Pisante

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

Analysis of PDEs 2014-12-30 v1

Authors: Giampiero Palatucci , Adriano Pisante

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).

Keywords

global compactness Palais-Smale sequences fractional Sobolev spaces profile decomposition bounded domain critical Sobolev embedding

Cite

@article{arxiv.1412.8392,
  title  = {A Global Compactness type result for Palais-Smale sequences in fractional Sobolev spaces},
  author = {Giampiero Palatucci and Adriano Pisante},
  journal= {arXiv preprint arXiv:1412.8392},
  year   = {2014}
}

Comments

To appear in Nonlinear Analysis: Theory, Methods & Applications

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