{
  "id": "2405.06304",
  "version": "v1",
  "published": "2024-05-10T08:19:35.000Z",
  "updated": "2024-05-10T08:19:35.000Z",
  "title": "An interpolation approach to $L^{\\infty}$ a priori estimates for elliptic problems with nonlinearity on the boundary",
  "authors": [
    "Maya Chhetri",
    "Nsoki Mavinga",
    "Rosa Pardo"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We establish an explicit $L^\\infty(\\Om)$ a priori estimate for weak solutions to subcritical elliptic problems with nonlinearity on the boundary, in terms of the powers of their $H^1(\\Om)$ norms. To prove our result, we combine in a novel way Moser type estimates together with elliptic regularity and Gagliardo--Nirenberg interpolation inequality. We illustrate our result with an application to subcritical problems satisfying Ambrosetti-Rabinowitz condition.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-10T08:19:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B45",
      "35J65",
      "35J61",
      "35J15"
    ],
    "keywords": [
      "elliptic problems",
      "priori estimate",
      "interpolation approach",
      "problems satisfying ambrosetti-rabinowitz condition",
      "nonlinearity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}