{
  "id": "1812.10093",
  "version": "v1",
  "published": "2018-12-25T11:40:01.000Z",
  "updated": "2018-12-25T11:40:01.000Z",
  "title": "A minimisation problem in ${\\mathrm{L}}^\\infty$ with PDE and unilateral constraints",
  "authors": [
    "Nikos Katzourakis"
  ],
  "comment": "26 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the minimisation of a cost functional which measures the misfit on the boundary of a domain between a component of the solution to a certain parametric elliptic PDE system and a prediction of the values of this solution. We pose this problem as a PDE-constrained minimisation problem for a supremal cost functional in ${\\mathrm{L}}^\\infty$, where except for the PDE constraint there is also a unilateral constraint on the parameter. We utilise approximation by PDE-constrained minimisation problems in ${\\mathrm{L}}^p$ as $p\\to\\infty$ and the generalised Kuhn-Tucker theory to derive the relevant variational inequalities in ${\\mathrm{L}}^p$ and ${\\mathrm{L}}^\\infty$. These results are motivated by the mathematical modelling of the novel bio-medical imaging method of Fluorescent Optical Tomography.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-25T11:40:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "unilateral constraint",
      "pde-constrained minimisation problem",
      "parametric elliptic pde system",
      "relevant variational inequalities",
      "supremal cost functional"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}