{
  "id": "2308.01642",
  "version": "v1",
  "published": "2023-08-03T09:19:00.000Z",
  "updated": "2023-08-03T09:19:00.000Z",
  "title": "Weak uniqueness by noise for singular stochastic PDEs",
  "authors": [
    "Federico Bertacco",
    "Carlo Orrieri",
    "Luca Scarpa"
  ],
  "categories": [
    "math.PR",
    "math.AP"
  ],
  "abstract": "We prove weak uniqueness for a general class of SPDEs on a Hilbert space. The main novelty is that the drift is only defined on a Sobolev-type subspace and no H\\\"older-continuity assumptions are required. This allows us to cover examples such as equations with divergence-form drift and Cahn-Hilliard-type equations with possibly singular perturbations. The main idea is to consider a suitable coloured Wiener noise so that both the solvability of the SPDE and the regularising effect of the Kolmogorov operator are preserved via stochastic maximal regularity results. As a by-product, this also allows us to generalise the available results of uniqueness by noise for perturbations of the heat equation to higher dimensions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-03T09:19:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "singular stochastic pdes",
      "weak uniqueness",
      "stochastic maximal regularity results",
      "hilbert space",
      "main novelty"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}