Equation \(\Delta u+K(x)e^{2u}=f(x)\) on \(R^ 2\) via stereographic projection

DOI10.1016/0022-247X(88)90324-1zbMath0722.35039MaRDI QIDQ756003

Chongwei Hong

Publication date: 1988

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

existenceflat metricprescribed Gauss curvature

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear boundary value problems for linear elliptic equations (35J65) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (1)

Two solutions to Kazdan-Warner’s problem on surfaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the equation \(\Delta u+Ke^{2u}=f\) and prescribed negative curvature in \({\mathbb{R}}^ 2\)
• On the elliptic equation \(\Delta \omega + K(x)e^{2\omega} = 0\) and conformal metrics with prescribed Gaussian curvatures
• A Best Constant and the Gaussian Curvature

This page was built for publication: Equation \(\Delta u+K(x)e^{2u}=f(x)\) on \(R^ 2\) via stereographic projection