Removable Singular Sets of Fully Nonlinear Elliptic Equations
MetadataShow full metadata
In this paper we consider fully nonlinear elliptic equations, including the Monge-Ampere equation and the Weingarden equation. We assume that
F(D2u,x) = ƒ(x) x ∈ Ω,
u(x) = g(x) x ∈ ∂Ω
has a solution u in C2(Ω) ∩ C(Ω¯), and
F(D2v(x), x) = ƒ(x) x ∈ Ω\S
v(x) = g(x) x ∈ ∂Ω
has a solution v in C2(Ω\S) ∩ Lip (Ω) ∩ C (Ω¯). We prove that under certain conditions on S and v, the singular set S is removable; i.e., u = v.
CitationWang, L., & Zhu, N. (1999). Removable singular sets of fully nonlinear elliptic equations. Electronic Journal of Differential Equations, 1999(04), pp. 1-5.
This work is licensed under a Creative Commons Attribution 4.0 International License.