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 language | English (US) |
|---|---|
| Pages (from-to) | 53-93 |
| Number of pages | 41 |
| Journal | Operator Theory: Advances and Applications |
| Volume | 236 |
| DOIs | |
| State | Published - 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