Prescribing scalar and boundary mean curvature on the three dimensional half sphere.(English)Zbl 1092.53028

Summary: We consider the problem of prescribing the scalar curvature and the boundary mean curvature of the standard half-three sphere, by deforming conformally its standard metric. Using blow-up analysis techniques and minimax arguments, we prove some existence and compactness results.

MSC:

 53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions 35B45 A priori estimates in context of PDEs 35J60 Nonlinear elliptic equations 53A30 Conformal differential geometry (MSC2010)
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