{
  "id": "2303.05310",
  "version": "v2",
  "published": "2023-03-09T14:58:50.000Z",
  "updated": "2023-07-11T11:21:05.000Z",
  "title": "The boundedness of stable solutions to semilinear elliptic equations with linear lower bound on nonlinearities",
  "authors": [
    "Fa Peng"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "Let $2\\le n\\le9$. Suppose that $f:R\\to R$ is locally Lipschitz function satisfying $f(t)\\ge A\\min\\{0,t\\}-K$ for all $t\\in R$ with some constant $A\\ge0$ and $K\\ge 0$. We establish an a priori interior H\\\"older regularity of $C^2$-stable solution to the semilinear elliptic equation $-\\Delta u=f(u)$. If, in addition, $f$ is nondecreasing and convex, we obtain the interior H\\\"older regularity of $W^{1,2}$-stable solutions. Note that the dimension $n\\le9$ is optimal.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2023-07-11T11:21:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "semilinear elliptic equation",
      "linear lower bound",
      "stable solution",
      "nonlinearities",
      "boundedness"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}