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Elliptic equations on convex domains with nonhomogeneous Dirichlet boundary conditions
Journal article   Open access   Peer reviewed

Elliptic equations on convex domains with nonhomogeneous Dirichlet boundary conditions

Dongsheng Li and Lihe Wang
Journal of Differential Equations, Vol.246(5), pp.1723-1743
2009
DOI: 10.1016/j.jde.2008.12.007
url
https://doi.org/10.1016/j.jde.2008.12.007View
Published (Version of record) Open Access

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.
Convex domain Differentiability Elliptic equation

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