{
  "id": "0804.4519",
  "version": "v1",
  "published": "2008-04-29T03:12:11.000Z",
  "updated": "2008-04-29T03:12:11.000Z",
  "title": "Cordes conditions and some alternatives for parabolic equations and discontinuous diffusion",
  "authors": [
    "Nikolai Dokuchaev"
  ],
  "comment": "18 pages",
  "journal": "Differential equations 33 (4), English translation: 1997, pp. 433-442, in Russian: 1996, pp. 552-531",
  "categories": [
    "math.AP",
    "math.PR"
  ],
  "abstract": "The paper considers parabolic equations in non-divergent form with discontinuous coefficients at higher derivatives. Their investigation is most complicated because, in general, in the case of discontinuous coefficients, the uniqueness of a solution for nonlinear parabolic or elliptic equations can fail, and there is no a priory estimate for partial derivatives of a solution. In this paper, existence and regularity results are obtained under some Cordes type restrictions on the coefficients. The results are applied to diffusion processes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-04-29T03:12:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K10",
      "60H10"
    ],
    "keywords": [
      "parabolic equations",
      "cordes conditions",
      "discontinuous diffusion",
      "alternatives",
      "discontinuous coefficients"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0804.4519D"
    }
  }
}