{
  "id": "2208.02527",
  "version": "v1",
  "published": "2022-08-04T08:47:43.000Z",
  "updated": "2022-08-04T08:47:43.000Z",
  "title": "Non-autonomous $L^q(L^p)$ maximal regularity for complex systems under mixed regularity in space and time",
  "authors": [
    "Sebastian Bechtel",
    "Fabian Gabel"
  ],
  "categories": [
    "math.AP",
    "math.CA"
  ],
  "abstract": "We show non-autonomous $L^q(L^p)$ maximal regularity for families of complex second-order systems in divergence form under a mixed H{\\\"o}lder regularity condition in space and time.To be more precise, we let $p,q \\in (1,\\infty)$ and we consider coefficient functions in $C^{\\beta + \\varepsilon}$ with values in $C^{\\alpha + \\varepsilon}$ subject to the parabolic relation $2\\beta + \\alpha = 1$.To this end, we provide a weak $(p,q)$-solution theory with uniform constants and establish a priori higher spatial regularity.Furthermore, we show $p$-bounds for semigroups and square roots generated by complex elliptic systems under a minimal regularity assumption for the coefficients.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-04T08:47:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "maximal regularity",
      "complex systems",
      "mixed regularity",
      "priori higher spatial regularity",
      "complex second-order systems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}