{
  "annotation_id": "45b97c88-87b6-45bd-b907-2aeefb27995d",
  "date_created": "2026-02-17T05:53:20.119000Z",
  "date_modified": "2026-02-17T05:53:20.119000Z",
  "file_hash": "cda3918c18412e831f5c35bcac86bbfda6121061f73c6d14425a406b95508531",
  "private": false,
  "record": {
    "abstract": "In this paper, we investigate the gradient estimates for solutions to the perfect conductivity problem with two closely spaced perfect conductors embedded in a homogeneous matrix, modeled by $p$-Laplacian elliptic equations. We first prove that the gradient of the solution remains bounded when the conductors possess partially ``flat\" boundaries. This contrasts with the case involving strictly convex inclusions, where the gradient can blow up. Second, for conductors with $C^{1,\\gamma}$ boundaries ($\\gamma\\in(0,1)$), we establish both upper and lower bounds on the gradient, with optimal blow-up rates. Furthermore, we provide precise asymptotic expansions in some special cases.",
    "arxiv_id": "2601.09435",
    "authors": [
      "Hongjie Dong",
      "Longjuan Xu"
    ],
    "categories": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Gradient estimates for the $p$-Laplacian perfect conductivity problem with partially flat and $C^{1,\\gamma}$ inclusions",
    "url": "https://arxiv.org/abs/2601.09435",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "19779fa6-9dbc-463e-ab1a-780648ce03dc",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}