{
  "id": "2309.07417",
  "version": "v1",
  "published": "2023-09-14T04:07:35.000Z",
  "updated": "2023-09-14T04:07:35.000Z",
  "title": "On the singular problem involving $g$-Laplacian",
  "authors": [
    "Kaushik Bal",
    "Riddhi Mishra",
    "Kaushik Mohanta"
  ],
  "comment": "15pp",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we show that the existence of a positive weak solution to the equation $(-\\Delta_g)^s u=f u^{-q(x)}\\;\\mbox{in}\\; \\Omega,$ where $\\Omega$ is a smooth bounded domain in $R^N$, $q\\in C^1(\\overline{\\Omega})$, and $(-\\Delta_g)^s$ is the fractional $g$-Laplacian with $g$ is the antiderivative of a Young function and $f$ in suitable Orlicz space subjected to zero Dirichlet condition. This includes the mixed fractional $(p,q)-$Laplacian as a special case. The solution so obtained is also shown to be locally H\\\"older continuous.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-14T04:07:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R11",
      "35J62"
    ],
    "keywords": [
      "singular problem",
      "zero dirichlet condition",
      "suitable orlicz space",
      "smooth bounded domain",
      "fractional"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}