{
  "id": "1502.06768",
  "version": "v1",
  "published": "2015-02-24T11:27:13.000Z",
  "updated": "2015-02-24T11:27:13.000Z",
  "title": "Blow-up solutions for some nonlinear elliptic equations involving a Finsler-Laplacian",
  "authors": [
    "Francesco Della Pietra",
    "Giuseppina di Blasio"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we prove existence results and asymptotic behavior for strong solutions $u\\in W^{2,2}_{\\textrm{loc}}(\\Omega)$ of the nonlinear elliptic problem \\begin{equation} \\tag{P} \\label{abstr} \\left\\{ \\begin{array}{ll} -\\Delta_{H}u+H(\\nabla u)^{q}+\\lambda u=f&\\text{in }\\Omega,\\\\ u\\rightarrow +\\infty &\\text{on }\\partial\\Omega, \\end{array} \\right. \\end{equation} where $H$ is a suitable norm of $\\mathbb R^{n}$, $\\Omega$ is a bounded domain, $\\Delta_{H}$ is the Finsler Laplacian, $1<q\\le 2$, $\\lambda>0$ and $f$ is a suitable function in $L^{\\infty}_{\\textrm{loc}}$. Furthermore, we are interested in the behavior of the solutions when $\\lambda\\rightarrow 0^{+}$, studying the so-called ergodic problem associated to \\eqref{abstr}. A key role in order to study the ergodic problem will be played by local gradient estimates for \\eqref{abstr}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-24T11:27:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J60",
      "35J25",
      "35B44"
    ],
    "keywords": [
      "nonlinear elliptic equations",
      "blow-up solutions",
      "finsler-laplacian",
      "ergodic problem",
      "local gradient estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}