The mixed problem in L p for some two-dimensional Lipschitz domains

Loredana Lanzani, Luca Capogna, Russell M. Brown

Research output: Contribution to journalArticle

14 Scopus citations

Abstract

We consider the mixed problem, {Δ u = 0 in Ω ∂u = f N on N u = fD on D in a class of Lipschitz graph domains in two dimensions with Lipschitz constant at most 1. We suppose the Dirichlet data, f D , has one derivative in L p (D) of the boundary and the Neumann data, f N , is in L p (N). We find a p 0 > 1 so that for p in an interval (1, p 0), we may find a unique solution to the mixed problem and the gradient of the solution lies in L p .

Original languageEnglish (US)
Pages (from-to)91-124
Number of pages34
JournalMathematische Annalen
Volume342
Issue number1
DOIs
StatePublished - Sep 1 2008
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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