Quasilinear elliptic equations with small boundary data

Chi ping Lau*

*Corresponding author for this work

Research output: Contribution to journalArticleResearchpeer-review

3 Citations (Scopus)

Abstract

It is shown that if the order of non-uniformity of a quasilinear elliptic equation is h, 1<h≤2, then the critical norm separating existence and non-existence of a solution to the Dirichlet problem with small boundary data is the {Mathematical expression} norm. For 0≤h≤1, existence of a solution is guaranteed without any smallness assumption on the given boundary data, provided that the usual a priori interior gradient bound for solution is available.

Original languageEnglish
Pages (from-to)77-99
Number of pages23
JournalManuscripta Mathematica
Volume53
Issue number1-2
DOIs
Publication statusPublished - 1 Feb 1985
Externally publishedYes

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