Removable Singular Sets of Fully Nonlinear Elliptic Equations
Date
1999-02-17
Authors
Wang, Lihe
Zhu, Ning
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
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.
Description
Keywords
Nonlinear PDE, Monge-Ampere equation, Removable singularity
Citation
Wang, L., & Zhu, N. (1999). Removable singular sets of fully nonlinear elliptic equations. Electronic Journal of Differential Equations, 1999(04), pp. 1-5.
Rights
Attribution 4.0 International
Rights Holder
This work is licensed under a Creative Commons Attribution 4.0 International License.