### Abstract

It is shown that if the order of non-uniformity of a quasi-linear elliptic equation is h,1<h≤2,then the critical norm separating existence and non-existence of a bounded solution to the exterior Dirichlet problem with small boundary data is the C^{0,2(h-1)/h} norm. For 0≤h≤1,existence of a bounded solution is guaranteed without any smallness assumption on the given boundary data.More precise information is given for the special case of the minimal surface equation.

Original language | English |
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Pages (from-to) | 53-62 |

Number of pages | 10 |

Journal | Manuscripta Mathematica |

Volume | 59 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Mar 1987 |

Externally published | Yes |