{
  "id": "2409.07027",
  "version": "v1",
  "published": "2024-09-11T05:46:50.000Z",
  "updated": "2024-09-11T05:46:50.000Z",
  "title": "Log-type ultra-analyticity of elliptic equations with gradient terms",
  "authors": [
    "Hongjie Dong",
    "Ming Wang"
  ],
  "comment": "24 pages, submitted",
  "categories": [
    "math.AP"
  ],
  "abstract": "It is well known that every solution of an elliptic equation is analytic if its coefficients are analytic. However, less is known about the ultra-analyticity of such solutions. This work addresses the problem of elliptic equations with lower-order terms, where the coefficients are entire functions of exponential type. We prove that every solution satisfies a quantitative logarithmic ultra-analytic bound and demonstrate that this bound is sharp. The results suggest that the ultra-analyticity of solutions to elliptic equations cannot be expected to achieve the same level of ultra-analyticity as the coefficients.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-09-11T05:46:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J15",
      "26E05",
      "35A20"
    ],
    "keywords": [
      "elliptic equation",
      "gradient terms",
      "log-type ultra-analyticity",
      "coefficients",
      "quantitative logarithmic ultra-analytic bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}