### 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 |

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### Cite this

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*Manuscripta Mathematica*, vol. 59, no. 1, pp. 53-62. https://doi.org/10.1007/BF01171264

**The exterior Dirichlet problem for quasi-linear elliptic equations with small boundary data.** / Lau, Chi ping.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - The exterior Dirichlet problem for quasi-linear elliptic equations with small boundary data

AU - Lau, Chi ping

PY - 1987/3/1

Y1 - 1987/3/1

N2 - It is shown that if the order of non-uniformity of a quasi-linear elliptic equation is h,10,2(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.

AB - It is shown that if the order of non-uniformity of a quasi-linear elliptic equation is h,10,2(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.

UR - http://www.scopus.com/inward/record.url?scp=34250101745&partnerID=8YFLogxK

U2 - 10.1007/BF01171264

DO - 10.1007/BF01171264

M3 - Article

VL - 59

SP - 53

EP - 62

JO - Manuscripta Mathematica

JF - Manuscripta Mathematica

SN - 0025-2611

IS - 1

ER -