{
  "id": "1812.04248",
  "version": "v1",
  "published": "2018-12-11T07:46:57.000Z",
  "updated": "2018-12-11T07:46:57.000Z",
  "title": "A profile decomposition for the limiting Sobolev embedding",
  "authors": [
    "Giuseppe Devillanova",
    "Cyril Tintarev"
  ],
  "categories": [
    "math.FA"
  ],
  "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 note we construct a profile decomposition for arbitrary sequences in the Sobolev space $H^{1,2}(M)$ of a compact Riemannian manifold, relative to the embedding of $H^{1,2}(M)$ into $L^{2^*}(M)$, generalizing the well-known profile decomposition of Struwe ([Proposition 2.1]{Struwe}) to the case of arbitrary bounded sequences.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-11T07:46:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E35",
      "46B50",
      "58J99",
      "35B44",
      "35A25"
    ],
    "keywords": [
      "profile decomposition",
      "limiting sobolev embedding",
      "compact riemannian manifold",
      "asymptotically disjoint supports plus",
      "arbitrary bounded sequences"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}