The existence and non-existence of a non-paeametric solution to equations of minimal sueface type

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Abstract

The Dirichlet problem for equations of minimal surface type 2 2 in a bounded C domain [formula omitted] is considered when the given boundary data are “small” and ∂Ω does not have the “correct” mean curvature. The critical norm separating existence and non-existence is found to be C0,1(∂Ω).

Original languageEnglish
Pages (from-to)177-196
Number of pages20
JournalAnalysis
Volume4
Issue number1-2
DOIs
Publication statusPublished - 1 Jan 1984
Externally publishedYes

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Minimal surface
Mean Curvature
Dirichlet Problem
Nonexistence
Norm

Cite this

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abstract = "The Dirichlet problem for equations of minimal surface type 2 2 in a bounded C domain [formula omitted] is considered when the given boundary data are “small” and ∂Ω does not have the “correct” mean curvature. The critical norm separating existence and non-existence is found to be C0,1(∂Ω).",
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The existence and non-existence of a non-paeametric solution to equations of minimal sueface type. / Lau, Chi Ping.

In: Analysis, Vol. 4, No. 1-2, 01.01.1984, p. 177-196.

Research output: Contribution to journalArticleResearchpeer-review

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AB - The Dirichlet problem for equations of minimal surface type 2 2 in a bounded C domain [formula omitted] is considered when the given boundary data are “small” and ∂Ω does not have the “correct” mean curvature. The critical norm separating existence and non-existence is found to be C0,1(∂Ω).

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