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.
A Profile Decomposition for the Limiting Sobolev Embedding / Devillanova, G.; Tintarev, C. - In: Fifteenth International Conference Zaragoza-Pau on Mathematics and its Applications / É. Ahusborde, C. Amrouche, G. Carbou, J. L. Gracia, M. C. López de Silanes, M. Palacios. - STAMPA. - Saragoza : PUZ - Prensas de la Universidad de Zaragoza, 2020. - ISBN 978-84-1340-039-6. - pp. 65-78
A Profile Decomposition for the Limiting Sobolev Embedding
G. Devillanova;
2020-01-01
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
