{
  "id": "2310.10194",
  "version": "v1",
  "published": "2023-10-16T09:01:47.000Z",
  "updated": "2023-10-16T09:01:47.000Z",
  "title": "Regularizing Effect for a Class of Maxwell-Schrödinger Systems",
  "authors": [
    "Ayana Pinheiro de Castro Santana",
    "Luís Henrique de Miranda"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we prove the existence and regularity of weak solutions for the following system \\begin{align*} \\begin{cases} -\\mbox{div}(M(x)\\nabla u) + g(x,u,v) = f \\ \\ \\mbox{in} \\ \\ \\Omega\\\\ -\\mbox{div}(M(x)\\nabla v) = h(x,u,v) \\ \\ \\mbox{in} \\ \\ \\Omega\\\\ \\ \\ \\ \\ \\ u=v=0 \\ \\ \\mbox{on} \\ \\ \\partial \\Omega, \\end{cases} \\end{align*} where $\\Omega$ is an open bounded subset of $\\mathbb{R}^N$, for $N>2$, $f\\in L^m(\\Omega)$, where $m>1$ and $h,\\ g$ are two Carath\\'eodory functions. We prove that under appropriate conditions on $g$ and $h$ there exist solutions which escape the predicted regularity by the classical Stampacchia's theory causing the so-called regularizing effect.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-16T09:01:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B65",
      "35D99"
    ],
    "keywords": [
      "regularizing effect",
      "maxwell-schrödinger systems",
      "open bounded subset",
      "weak solutions",
      "caratheodory functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}