{
  "annotation_id": "bbec7ae1-4fea-4a81-83df-0400ba906bb7",
  "date_created": "2026-02-17T05:53:15.636000Z",
  "date_modified": "2026-02-17T05:53:15.636000Z",
  "file_hash": "7af6c9f3984e880707192acf6c462f240b97437fc943eed033882ba5828141d3",
  "private": false,
  "record": {
    "abstract": "A quantitative regularity theory is developed for weak solutions to the parabolic system $$ \\partial_t u-\\mathrm{div}\\,{\\boldsymbol{\\mathsf A}}(x,t,Du)=0 \\quad\\text{in }E_T\\subset \\mathbb{R}^N\\times\\mathbb{R}, $$ which features the $p$-Laplacian with measurable coefficients. We focus on the sub-critical range $1\u003cp\\le \\tfrac{2N}{N+2}$ and obtain two main results. \\emph{Local boundedness:} starting from an $L^{\\boldsymbol{\\mathsf r}}$-control of $u$ with ${\\boldsymbol{\\mathsf r}}\u003e\\frac{N(2-p)}{p}$, we derive sharp, scale-invariant $L^\\infty$-estimates. \\emph{Higher integrability of the gradient:} $|Du|$ self-improves from $L^p_{\\mathrm{loc}}$ to $L^{p(1+\\varepsilon)}_{\\mathrm{loc}}$ for some $\\varepsilon\u003e0$ depending only on the data. The same results still hold given proper source terms.",
    "arxiv_id": "2601.08466",
    "authors": [
      "Verena B\u00f6gelein",
      "Frank Duzaar",
      "Ugo Gianazza",
      "Naian Liao"
    ],
    "categories": [
      "math.AP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Regularity theory for sub-critical $p$-parabolic systems with measurable coefficients",
    "url": "https://arxiv.org/abs/2601.08466",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "4176ed2f-4f0c-4ae5-9528-d5e1107dcd62",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}