{
  "id": "1702.06718",
  "version": "v1",
  "published": "2017-02-22T09:23:46.000Z",
  "updated": "2017-02-22T09:23:46.000Z",
  "title": "On existence and concentration of solutions to a class of quasilinear problems involving the $1-$Laplace operator",
  "authors": [
    "C. O. Alves",
    "M. T. O. Pimenta"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this work we use variational methods to prove results on existence and concentration of solutions to a problem in $\\mathbb{R}^N$ involving the $1-$Laplacian operator. A thorough analysis on the energy functional defined in the space of functions of bounded variation $BV(\\mathbb{R}^N)$ is necessary, where the lack of compactness is overcome by using the Concentration of Compactness Principle of Lions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-22T09:23:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J62",
      "35J20"
    ],
    "keywords": [
      "quasilinear problems",
      "laplace operator",
      "concentration",
      "laplacian operator",
      "compactness principle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}