On second-order and fourth-order elliptic systems consisting of bulk and surface PDEs: Well-posedness, regularity theory and eigenvalue problems

Patrik Knopf, Chun Liu

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

In this paper, we study second-order and fourth-order elliptic problems which include not only a Poisson equation in the bulk but also an inhomogeneous Laplace Beltrami equation on the boundary of the domain. The bulk and the surface PDE are coupled by a boundary condition that is either of Dirichlet or Robin type. We point out that both the Dirichlet and the Robin type boundary condition can be handled simultaneously through our formalism without having to change the framework. Moreover, we investigate the eigenvalue problems associated with these second-order and fourth-order elliptic systems.We further discuss the relation between these elliptic problems and certain parabolic problems, especially the Allen Cahn equation and the Cahn Hilliard equation with dynamic boundary conditions.

Original languageEnglish (US)
Pages (from-to)507-533
Number of pages27
JournalInterfaces and Free Boundaries
Volume23
Issue number4
DOIs
StatePublished - 2021

All Science Journal Classification (ASJC) codes

  • Applied Mathematics

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