The Dirichlet and Regularity Problems for Some Second Order Linear Elliptic Systems on Bounded Lipschitz Domains

Nguyen T Nguyen*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

In this paper, we investigate divergence-form linear elliptic systems on bounded Lipschitz domains in ℝ d + 1 , d≥ 2 , with L 2 boundary data. The coefficients are assumed to be real, bounded, and measurable. We show that when the coefficients are small, in Carleson norm, compared to one that is continuous on the boundary, we obtain solvability for both the Dirichlet and regularity boundary value problems given that the coefficients satisfy a certain “pseudo-symmetry” condition.

Original languageEnglish (US)
Pages (from-to)167-186
Number of pages20
JournalPotential Analysis
Volume45
Issue number1
DOIs
StatePublished - Jul 1 2016

Keywords

  • Bounded Lipschitz domains
  • Linear elliptic systems
  • Second order
  • Small Carleson norm condition

ASJC Scopus subject areas

  • Analysis

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