The Liouville equation in a half-plane

DOI10.1016/J.JDE.2009.03.012zbMath1173.35059OpenAlexW2008108704WikidataQ56885372 ScholiaQ56885372MaRDI QIDQ1019663

José A. Gálvez, Pablo Mira

Publication date: 4 June 2009

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2009.03.012

zbMATH Keywords

classification theoremLiouville equationhalf-planepunctured disc

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Second-order elliptic equations (35J15)

Related Items (12)

Conformal metrics with prescribed gaussian and geodesic curvatures ⋮ Local and Nonlocal Singular Liouville Equations in Euclidean Spaces ⋮ Conformal metrics with prescribed scalar and mean curvature ⋮ Prescribing Gaussian and geodesic curvature on disks ⋮ The nonlocal Liouville-type equation in \(\mathbb {R}\) and conformal immersions of the disk with boundary singularities ⋮ A double mean field equation related to a curvature prescription problem ⋮ The Liouville equation in an annulus ⋮ Blow-up analysis of conformal metrics of the disk with prescribed Gaussian and geodesic curvatures ⋮ The geometric Neumann problem for the Liouville equation ⋮ Large conformal metrics with prescribed Gaussian and geodesic curvatures ⋮ Uniqueness theorems for fully nonlinear conformal equations on subdomains of the sphere ⋮ Minding's theorem for low degrees of differentiability

Cites Work

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• Metrics of constant curvature on a Riemann surface with two corners on the boundary
• Liouville-type theorems and harnack-type inequalities for semilinear elliptic equations
• Classification of solutions of some nonlinear elliptic equations
• Asymptotic radial symmetry for solutions of \(\Delta u+e^ u=0\) in a punctured disc
• Classification of conformal metrics on \(\mathbb R^2_+\) with constant Gauss curvature and geodesic curvature on the boundary under various integral finiteness assumptions
• Liouville's formula in arbitrary planar domains
• On the solutions to some elliptic equations with nonlinear Neumann boundary conditions
• Uniqueness theorems through the method of moving spheres
• The Cauchy problem for the Liouville equation and Bryant surfaces
• A new approach to some nonlinear geometric equations in dimension two
• A uniqueness theorem for harmonic functions on the upper-half plane
• Layer solutions in a half‐space for boundary reactions

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