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

Chi ping Lau

doi:10.1007/BF01171264

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

Chi ping Lau^*

^*Corresponding author for this work

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

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
Pages (from-to)	53-62
Number of pages	10
Journal	Manuscripta Mathematica
Volume	59
Issue number	1
DOIs	https://doi.org/10.1007/BF01171264
Publication status	Published - 1 Mar 1987
Externally published	Yes

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

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