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On second-order and fourth-order elliptic systems consisting of bulk and surface PDEs: Well-posedness, regularity theory and eigenvalue problems
- Source :
- Interfaces and Free Boundaries. 23:507-533
- Publication Year :
- 2021
- Publisher :
- European Mathematical Society - EMS - Publishing House GmbH, 2021.
-
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.
- Subjects :
- 35J57, 35J58, 35P05, 58J05, 58J50
Surface (mathematics)
Applied Mathematics
010102 general mathematics
Mathematical analysis
Mathematics::Analysis of PDEs
Boundary (topology)
Mathematics::Spectral Theory
Type (model theory)
01 natural sciences
Domain (mathematical analysis)
Dirichlet distribution
Mathematics - Spectral Theory
010101 applied mathematics
symbols.namesake
Mathematics - Analysis of PDEs
FOS: Mathematics
symbols
Boundary value problem
0101 mathematics
Poisson's equation
Spectral Theory (math.SP)
Eigenvalues and eigenvectors
Analysis of PDEs (math.AP)
Mathematics
Subjects
Details
- ISSN :
- 14639963
- Volume :
- 23
- Database :
- OpenAIRE
- Journal :
- Interfaces and Free Boundaries
- Accession number :
- edsair.doi.dedup.....b3d31b602c1e0886e053eb90f5c624c6