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On compact subsets of Sobolev spaces on manifolds
Leszek Skrzypczak, Cyril Tintarev
It is common that a Sobolev space defined on has a non-compact embedding into an -space, but it has subspaces for which this embedding becomes compact. There ar…
Profile decomposition of Struwe-Solimini for manifolds with bounded geometry
Kunnath Sandeep, Cyril TIntarev
For many known non-compact embeddings of two Banach spaces , every bounded sequence in has a subsequence that takes form of a \emph{profile decomposition} -…
A profile decomposition for the limiting Sobolev embedding
Giuseppe Devillanova, Cyril Tintarev
For many known non-compact embeddings of two Banach spaces , every bounded sequence in has a subsequence that takes form of a profile decomposition - a sum…
Defect of compactness for Sobolev spaces on manifolds with bounded geometry
Leszek Skrzypczak, Cyril Tintarev
Defect of compactness, relative to an embedding of two Banach spaces E and F, is a difference between a weakly convergent sequence in E and its weak limit taken up to a remainder t…
On defect of compactness for Sobolev spaces on manifolds
Leszek Skrzypczak, Cyril Tintarev
Defect of compactness, relative to an embedding of two Banach spaces E and F, is a difference between a weakly convergent sequence in E and its weak limit taken up to a remainder t…
Concentration analysis in Banach spaces
Sergio Solimini, Cyril Tintarev
The concept of a profile decomposition formalizes concentration compactness arguments on the functional-analytic level, providing a powerful refinement of the Banach-Alaoglu weak-s…