For many known non-compact embeddings of two Banach spaces E ,! F, every bounded sequence in E has a subsequence that takes the form of a profile decomposition - a sum of clearly structured terms with asymptotically disjoint supports plus a remainder that vanishes in the norm of F. In this note we construct a profile decomposition for arbitrary sequences in the Sobolev space H1;2(M) of a compact Riemannian manifold, relative to the embedding of H1;2(M) into L^2 (M), generalizing the well-known profile decomposition of Struwe [12, Proposition 2.1] to the case of arbitrary bounded sequences.
|Titolo:||A Profile Decomposition for the Limiting Sobolev Embedding|
|Titolo del libro:||Fifteenth International Conference Zaragoza-Pau on Mathematics and its Applications|
|Editore:||PUZ - Prensas de la Universidad de Zaragoza|
|Data di pubblicazione:||2020|
|Appare nelle tipologie:||2.1 Contributo in volume (Capitolo o Saggio)|