{
  "id": "2003.05298",
  "version": "v1",
  "published": "2020-03-11T13:56:22.000Z",
  "updated": "2020-03-11T13:56:22.000Z",
  "title": "A space-time relaxation for $L^1$ optimal control problems",
  "authors": [
    "Malte Kampschulte"
  ],
  "comment": "17 pages",
  "categories": [
    "math.OC",
    "math.AP"
  ],
  "abstract": "We introduce a vertical type relaxation for optimal control problems which only have $L^1$-coercivity for their controls. Usually such problems feature both concentration and oscillation effects at the same time. We propose relaxing to an associated problem in space-time, where the controls can be considered bounded in $L^\\infty$, greatly simplifying any analysis. In this relaxation, concentrations are transformed into vertical parts and oscillations can be dealt with using Young-measures. This technique can be extended to similar problems on infinite-dimensional spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-11T13:56:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49J45",
      "49J15",
      "49J20"
    ],
    "keywords": [
      "optimal control problems",
      "space-time relaxation",
      "vertical type relaxation",
      "similar problems",
      "problems feature"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}