Profile decomposition of Struwe-Solimini for manifolds with bounded geometry

2019/01/29 by Kunnath Sandeep, Sandeep, Kunnath, Cyril Tintarev +2
Computer Science · Mathematics · #35A25 #35B44 #46B50 #46E35 #58J99 #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations #math.FA #msc:35A25 #msc:35B44 #msc:46B50 #msc:46E35 #msc:58J99

paper · pdf · doi:10.48550/arxiv.1901.10427

arxiv created 2019/01/29 · openalex publication_date 2019/01/29 · arxiv updated 2019/01/30 · openalex created_date 2019/02/21 · openalex updated_date 2026/07/28

Abstract

For many known non-compact embeddings of two Banach spaces E\hookrightarrow F, every bounded sequence in E has a subsequence that takes 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 paper we construct a profile decomposition for arbitrary sequences in the Sobolev space H^1,2(M) of a Riemannian manifold with bounded geometry, relative to the embedding of H^1,2(M) into L^{2^*}(M), generalizing the well-known profile decomposition of Struwe to the case of any bounded sequence and a non-compact manifold.

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