{
  "id": "2003.03782",
  "version": "v1",
  "published": "2020-03-08T13:40:13.000Z",
  "updated": "2020-03-08T13:40:13.000Z",
  "title": "An $L_p$-estimate for the stochastic heat equation on angular domains in $\\mathbb{R}^2$ with mixed weights",
  "authors": [
    "Petru A. Cioica-Licht"
  ],
  "categories": [
    "math.PR",
    "math.AP"
  ],
  "abstract": "We establish a refined $L_p$-estimate ($p\\geq 2$) for the stochastic heat equation on angular domains in $\\mathbb{R}^2$ with mixed weights based on both, the distance to the boundary and the distance to the vertex. This way we can capture both causes for singularities of the solution: the incompatibility of noise and boundary condition on the one hand and the influence of boundary singularities (here, the vertex) on the other hand.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-08T13:40:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "35R60",
      "35K05"
    ],
    "keywords": [
      "stochastic heat equation",
      "angular domains",
      "mixed weights",
      "boundary singularities",
      "boundary condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}