Escobar's Type Theorems for elliptic fully nonlinear degenerate equations

2016/06/24 by D. P. Abanto, Abanto, D. P., J. M. Espinar +1
Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #math.AP #math.DG

paper · pdf · doi:10.48550/arxiv.1606.07530

arxiv created 2016/06/24 · arxiv updated 2016/06/27

Abstract

In this paper we prove non-existence and classification results for elliptic fully nonlinear elliptic degenerate conformal equations on certain subdomains of the sphere with prescribed constant mean curvature along its boundary. We also consider non-degenerate equations. Such subdomains are the hemisphere (or a geodesic ball in \mathbbS^m), punctured balls and annular domains. Our results extend those of Escobar in when m≥ 3, and Hang-Wang and Jimenez in when m=2.

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