{
  "id": "2104.02795",
  "version": "v1",
  "published": "2021-04-06T21:26:23.000Z",
  "updated": "2021-04-06T21:26:23.000Z",
  "title": "Besov regularity for a class of singular or degenerate elliptic equations",
  "authors": [
    "Pasquale Ambrosio"
  ],
  "categories": [
    "math.AP",
    "math.CA"
  ],
  "abstract": "Motivated by applications to congested traffic problems, we establish higher integrability results for the gradient of local weak solutions to the strongly degenerate elliptic PDE $-\\mathrm{div}\\left((\\vert\\nabla u\\vert-1)_{+}^{q-1}\\frac{\\nabla u}{\\vert\\nabla u\\vert}\\right)=f,\\,\\,\\mathrm{in}\\,\\,\\Omega$, where $\\Omega$ is a bounded domain in $\\mathbb{R}^{n}$ for $n\\geq2$, $1<q<\\infty$ and $\\left(\\,\\cdot\\,\\right)_{+}$ stands for the positive part. We assume that the datum $f$ belongs to a suitable Sobolev or Besov space. The main novelty here is that we deal with the case of subquadratic growth, i.e. $1<q<2$, which has so far been neglected. We also infer the higher integrability of the solution to a variational problem, which is characterized by the above equation. For the sake of completeness, we finally give a Besov regularity result also in the case $q\\geq2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-06T21:26:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B65",
      "35J70",
      "35J75",
      "49N60"
    ],
    "keywords": [
      "degenerate elliptic equations",
      "establish higher integrability results",
      "local weak solutions",
      "strongly degenerate elliptic pde",
      "besov regularity result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}