Concentration Compactness: Functional-analytic Grounds And Applications

By Kyril Tintarev, K. Fieseler. 2007

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A Global Compactness type result for Palais-Smale sequences in fractional Sobolev spaces (2014, methodology): “y to several extensions and to a huge number of applications, e.g. in the case of problems involving biharmonic and polyharmonic operators but also in other more complicated problems (see e. g. [18], [19] and the references therein). In order to state precisely our main result, consider the followin”
Improved Sobolev embeddings, profile decomposition, and concentration-compactness for fractional Sobolev spaces (2013, methodology): “The previous result extends to the case of the fractional spaces Ḣs a well known fact for s = 1 and, more generally, when s is an integer (see [31] and [32]; see also [50] and the references therein); namely that, at least locally, compactness in the Sobolev embedding fails precisely because of conc”