{
  "id": "1506.09105",
  "version": "v1",
  "published": "2015-06-30T14:25:19.000Z",
  "updated": "2015-06-30T14:25:19.000Z",
  "title": "On Yamabe type problems on Riemannian manifolds with boundary",
  "authors": [
    "Marco Ghimenti",
    "Anna Maria Micheletti",
    "Angela Pistoia"
  ],
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "Let $(M,g)$ be a $n-$dimensional compact Riemannian manifold with boundary. We consider the Yamabe type problem \\begin{equation} \\left\\{ \\begin{array}{ll} -\\Delta_{g}u+au=0 & \\text{ on }M \\\\ \\partial_\\nu u+\\frac{n-2}{2}bu= u^{{n\\over n-2}\\pm\\varepsilon} & \\text{ on }\\partial M \\end{array}\\right. \\end{equation} where $a\\in C^1(M),$ $b\\in C^1(\\partial M)$, $\\nu$ is the outward pointing unit normal to $\\partial M $ and $\\varepsilon$ is a small positive parameter. We build solutions which blow-up at a point of the boundary as $\\varepsilon$ goes to zero. The blowing-up behavior is ruled by the function $b-H_g ,$ where $H_g$ is the boundary mean curvature.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-30T14:25:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "yamabe type problem",
      "dimensional compact riemannian manifold",
      "boundary mean curvature",
      "outward pointing unit normal",
      "small positive parameter"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150609105G"
    }
  }
}