Boundary-value problems for higher-order elliptic equations in non-smooth domains

Ariel Barton, Svitlana Mayboroda

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

This paper presents a survey of recent results, methods, and open problems in the theory of higher-order elliptic boundary value problems on Lipschitz and more general non-smooth domains. The main topics include the maximum principle and pointwise estimates on solutions in arbitrary domains, analogues of the Wiener test governing continuity of solutions and their derivatives at a boundary point, and well-posedness of boundary value problems in domains with Lipschitz boundaries.

Original languageEnglish (US)
Pages (from-to)53-93
Number of pages41
JournalOperator Theory: Advances and Applications
Volume236
DOIs
StatePublished - 2014

Bibliographical note

Publisher Copyright:
© 2014 Springer Basel.

Keywords

  • Biharmonic equation
  • Dirichlet problem
  • General domains
  • Higher-order equation
  • Lipschitz domain
  • Maximum principle
  • Neumann problem
  • Polyharmonic equation
  • Regularity problem
  • Wiener criterion

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