{
  "id": "1809.04674",
  "version": "v1",
  "published": "2018-09-12T21:02:41.000Z",
  "updated": "2018-09-12T21:02:41.000Z",
  "title": "Boundary value problems in Lipschitz domains for equations with lower order coefficients",
  "authors": [
    "Georgios Sakellaris"
  ],
  "comment": "50 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We use the method of layer potentials to study the $R_2$ Regularity problem and the $D_2$ Dirichlet problem for second order elliptic equations of the form $\\mathcal{L}u=0$, with lower order coefficients, in bounded Lipschitz domains. For $R_2$ we establish existence and uniqueness assuming that $\\mathcal{L}$ is of the form $\\mathcal{L}u=-\\text{div}(A\\nabla u+bu)+c\\nabla u+du$, where the matrix $A$ is uniformly elliptic and H\\\"older continuous, $b$ is H\\\"older continuous, and $c,d$ belong to Lebesgue classes and they satisfy either the condition $d\\geq\\text{div}b$, or $d\\geq\\text{div}c$ in the sense of distributions. In particular, $A$ is not assumed to be symmetric, and there is no smallness assumption on the norms of the lower order coefficients. We also show existence and uniqueness for $D_2$ for the adjoint equations $\\mathcal{L}^tu=0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-12T21:02:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lower order coefficients",
      "boundary value problems",
      "lipschitz domains",
      "second order elliptic equations",
      "layer potentials"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 50,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}