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. <i>Electronic Journal of Differential Equations, 1999</i>(04), pp. 1-5.

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Attribution 4.0 International

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This work is licensed under a Creative Commons Attribution 4.0 International License.

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