{
  "id": "2102.01550",
  "version": "v1",
  "published": "2021-02-02T15:24:14.000Z",
  "updated": "2021-02-02T15:24:14.000Z",
  "title": "On the continuity of solutions of quasilinear parabolic equations with generalized Orlicz growth under non-logarithmic conditions",
  "authors": [
    "Igor I. Skrypnik",
    "Mykhailo V. Voitovych"
  ],
  "comment": "32 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove the continuity of bounded solutions for a wide class of parabolic equations with $(p,q)$-growth $$ u_{t}-{\\rm div}\\left(g(x,t,|\\nabla u|)\\,\\frac{\\nabla u}{|\\nabla u|}\\right)=0, $$ under the generalized non-logarithmic Zhikov's condition $$ g(x,t,{\\rm v}/r)\\leqslant c(K)\\,g(y,\\tau,{\\rm v}/r), \\quad (x,t), (y,\\tau)\\in Q_{r,r}(x_{0},t_{0}), \\quad 0<{\\rm v}\\leqslant K\\lambda(r), $$ $$ \\quad \\lim\\limits_{r\\rightarrow0}\\lambda(r)=0, \\quad \\lim\\limits_{r\\rightarrow0} \\frac{\\lambda(r)}{r}=+\\infty, \\quad \\int_{0} \\lambda(r)\\,\\frac{dr}{r}=+\\infty. $$ In particular, our results cover new cases of double-phase parabolic equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-02T15:24:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B65",
      "35D30",
      "35K59",
      "35K92"
    ],
    "keywords": [
      "quasilinear parabolic equations",
      "generalized orlicz growth",
      "non-logarithmic conditions",
      "continuity",
      "double-phase parabolic equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}