{
  "id": "0807.3810",
  "version": "v1",
  "published": "2008-07-24T07:49:41.000Z",
  "updated": "2008-07-24T07:49:41.000Z",
  "title": "On derivation of Euler-Lagrange Equations for incompressible energy-minimizers",
  "authors": [
    "Nirmalendu Chaudhuri",
    "Aram L. Karakhanyan"
  ],
  "comment": "23 pages",
  "categories": [
    "math.AP",
    "math.CA"
  ],
  "abstract": "We prove that any distribution $q$ satisfying the equation $\\nabla q=\\div{\\bf f}$ for some tensor ${\\bf f}=(f^i_j), f^i_j\\in h^r(U)$ ($1\\leq r<\\infty$) -the {\\it local Hardy space}, $q$ is in $h^r$, and is locally represented by the sum of singular integrals of $f^i_j$ with Calder\\'on-Zygmund kernel. As a consequence, we prove the existence and the local representation of the hydrostatic pressure $p$ (modulo constant) associated with incompressible elastic energy-minimizing deformation ${\\bf u}$ satisfying $|\\nabla {\\bf u}|^2, |{\\rm cof}\\nabla{\\bf u}|^2\\in h^1$. We also derive the system of Euler-Lagrange equations for incompressible local minimizers ${\\bf u}$ that are in the space $K^{1,3}_{\\rm loc}$; partially resolving a long standing problem. For H\\\"older continuous pressure $p$, we obtain partial regularity of area-preserving minimizers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-07-24T07:49:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J60",
      "42A40",
      "73C50",
      "73V25"
    ],
    "keywords": [
      "euler-lagrange equations",
      "incompressible energy-minimizers",
      "derivation",
      "local hardy space",
      "singular integrals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0807.3810C"
    }
  }
}