Conformal metrics of the disk with prescribed Gaussian and geodesic curvatures

Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Nonlinear boundary value problems for nonlinear elliptic equations (35J66) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91)

Cites Work

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Prescribing the Gaussian curvature in a subdomain of \(\mathbb {S}^2\) with Neumann boundary condition
Blow-up analysis of a nonlocal Liouville-type equation
On prescribing geodesic curvature on \(D^2\)
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Problèmes de Neumann non linéaires sur les variétés riemanniennes
Hypersurfaces in \(\mathbb H^{n+1}\) and conformally invariant equations: the generalized Christoffel and Nirenberg problems
Sur les transformations conformes des variétés riemanniennes à bord. (On conformal transformations of Riemannian manifolds with boundary)
The Liouville equation in a half-plane
Prescribing Gaussian curvature on S 2
Conformal deformations of metric on \({\mathcal S}\) 2
Extremals of determinants of Laplacians
Prescribing Gaussian curvatures on surfaces with conical singularities
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Meilleures constantes dans le théorème d'inclusion de Sobolev et un théorème de Fredholm non linéaire pour la transformation conforme de la courbure scalaire
The scalar curvature equation on 2- and 3-spheres
Classification of conformal metrics on \(\mathbb R^2_+\) with constant Gauss curvature and geodesic curvature on the boundary under various integral finiteness assumptions
A family of curvature flows on surfaces with boundary
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Prescribing Gaussian and geodesic curvature on disks
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Large conformal metrics with prescribed Gaussian and geodesic curvatures
Curvature functions for compact 2-manifolds
Riemannian structures of prescribed Gaussian curvature for compact 2- manifolds
A flow approach to Nirenberg's problem
Blow-up analysis of conformal metrics of the disk with prescribed Gaussian and geodesic curvatures
BLOW-UP ANALYSIS FOR SOLUTIONS OF THE LAPLACIAN EQUATION WITH EXPONENTIAL NEUMANN BOUNDARY CONDITION IN DIMENSION TWO
Scalar Curvatures on S 2
Uniform estimates and blow–up behavior for solutions of −δ(u)=v(x)e^uin two dimensions
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A necessary and sufficient condition for the nirenberg problem
Conformal metrics with prescribed gaussian and geodesic curvatures
ON NIRENBERG'S PROBLEM
A prescribing geodesic curvature problem

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