On the elliptic equation Δu + K(x)e2u = 0 on B2

Sanxing Wu; Hongying Liu

doi:10.1090/S0002-9939-04-07366-6

On the elliptic equation Δu + K(x)e^2u = 0 on B²

Sanxing Wu^*
, Hongying Liu

^*Corresponding author for this work

School of Mathematical Sciences

Beihang University

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

In this paper we consider the existence problem for the elliptic equation Δu + K(x)e^2u = 0 on B² = {x ε R² | |x| < 1}, which arises in the study of conformal deformation of the hyperbolic disc. We prove an existence result for the above equation.

Original language	English
Pages (from-to)	3083-3088
Number of pages	6
Journal	Proceedings of the American Mathematical Society
Volume	132
Issue number	10
DOIs	https://doi.org/10.1090/S0002-9939-04-07366-6
State	Published - Oct 2004

Keywords

Conformal Riemannian metric
Gaussian curvature
Semilinear elliptic PDE

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title = "On the elliptic equation Δu + K(x)e2u = 0 on B2",

abstract = "In this paper we consider the existence problem for the elliptic equation Δu + K(x)e2u = 0 on B2 = \{x ε R2 | |x| < 1\}, which arises in the study of conformal deformation of the hyperbolic disc. We prove an existence result for the above equation.",

keywords = "Conformal Riemannian metric, Gaussian curvature, Semilinear elliptic PDE",

author = "Sanxing Wu and Hongying Liu",

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N2 - In this paper we consider the existence problem for the elliptic equation Δu + K(x)e2u = 0 on B2 = {x ε R2 | |x| < 1}, which arises in the study of conformal deformation of the hyperbolic disc. We prove an existence result for the above equation.

AB - In this paper we consider the existence problem for the elliptic equation Δu + K(x)e2u = 0 on B2 = {x ε R2 | |x| < 1}, which arises in the study of conformal deformation of the hyperbolic disc. We prove an existence result for the above equation.

KW - Conformal Riemannian metric

KW - Gaussian curvature

KW - Semilinear elliptic PDE

UR - https://www.scopus.com/pages/publications/5644248266

U2 - 10.1090/S0002-9939-04-07366-6

DO - 10.1090/S0002-9939-04-07366-6

M3 - 文章

AN - SCOPUS:5644248266

SN - 0002-9939

VL - 132

SP - 3083

EP - 3088

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 10

ER -

On the elliptic equation Δu + K(x)e^2u = 0 on B²

Abstract

Keywords

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