A Harnack-Type Inequality for a Prescribed-Curvature Equation on a Domain with Boundary

DOI10.1515/ANS-2014-0311zbMath1309.35028arXiv1309.1135OpenAlexW2963529337MaRDI QIDQ2923161

Mathew R. Gluck, Lei Zhang, Ying Guo

Publication date: 15 October 2014

Published in: Advanced Nonlinear Studies (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1309.1135

zbMATH Keywords

semilinear elliptic equationboundary Yamabe problem

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Semilinear elliptic equations (35J61) Positive solutions to PDEs (35B09)

Cites Work

• Compactness of solutions to the Yamabe problem. III
• A compactness theorem for the Yamabe problem
• Blow-up phenomena for the Yamabe equation. II
• Liouville-type theorems and harnack-type inequalities for semilinear elliptic equations
• Conformal deformation of a Riemannian metric to constant scalar curvature
• Conformal deformation of a Riemannian metric to a scalar flat metric with constant mean curvature on the boundary
• The Yamabe problem on manifolds with boundary
• Compactness results in conformal deformations of Riemannian metrics on manifolds with boundaries
• Prescribing scalar and boundary mean curvature on the three dimensional half sphere
• Refined asymptotic estimates for conformal scalar curvature equation via moving sphere method
• Blow-up phenomena for the Yamabe equation
• Asymptotic symmetry and local behavior of semilinear elliptic equations with critical sobolev growth
• Estimates of the conformal scalar curvature equation via the method of moving planes
• The existence of conformal metrics with constant scalar curvature and constant boundary mean curvature

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