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

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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 C0,2(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 languageEnglish
Pages (from-to)53-62
Number of pages10
JournalManuscripta Mathematica
Volume59
Issue number1
DOIs
Publication statusPublished - 1 Mar 1987
Externally publishedYes

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Exterior Problem
Quasilinear Elliptic Equation
Bounded Solutions
Dirichlet Problem
Norm
Non-uniformity
Minimal surface
Nonexistence

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

In: Manuscripta Mathematica, Vol. 59, No. 1, 01.03.1987, p. 53-62.

Research output: Contribution to journalArticleResearchpeer-review

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