Journal article
Elliptic equations on convex domains with nonhomogeneous Dirichlet boundary conditions
Journal of Differential Equations, Vol.246(5), pp.1723-1743
2009
DOI: 10.1016/j.jde.2008.12.007
Abstract
In this paper, we will study the differentiability on the boundary of solutions of elliptic non-divergence differential equations on convex domains. The results are divided into two cases: (i) at the boundary points where the blow-up of the domain is not the half-space, if the boundary function is differentiable then the solution is differentiable; (ii) at the boundary points where the blow-up of the domain is the half-space, the differentiability of the solution needs an extra Dini condition for the boundary function. Counterexample is given to show that our results are optimal.
Details
- Title: Subtitle
- Elliptic equations on convex domains with nonhomogeneous Dirichlet boundary conditions
- Creators
- Dongsheng Li - College of Science, Xi'an Jiaotong University, Xi'an 710049, ChinaLihe Wang - Department of Mathematics, University of Iowa, 14 Maclean Hall, Iowa City, IA 52242-1419, USA
- Resource Type
- Journal article
- Publication Details
- Journal of Differential Equations, Vol.246(5), pp.1723-1743
- DOI
- 10.1016/j.jde.2008.12.007
- ISSN
- 0022-0396
- eISSN
- 1090-2732
- Publisher
- Elsevier Inc
- Language
- English
- Date published
- 2009
- Academic Unit
- Mathematics
- Record Identifier
- 9984083258702771
Metrics
23 Record Views