Layer potentials and boundary value problems for Laplacian in Lipschitz domains with data in quasi-Banach Besov spaces

Svetlana Mayboroda, Marius Mitrea

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

We study the Dirichlet and Neumann boundary value problems for the Laplacian in a Lipschitz domain Ω, with boundary data in the Besov space Bp,p s (∂Ω). The novelty is to identify a way of measuring smoothness for the solution u that allows us to consider the case p < 1. This is accomplished by using a Besov-based nontangential maximal function in place of the classical one. This builds on the works of Jerison and Kenig [14], where the case p > 1 was treated.

Original languageEnglish (US)
JournalAnnali di Matematica Pura ed Applicata
Volume185
Issue number2
DOIs
StatePublished - Jan 1 2006

Keywords

  • Besov space regularity
  • Elliptic PDE
  • Layer potentials
  • Lipschitz domains
  • Smoothness

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