Existence and extendibility of rotationally symmetric graphs with a prescribed higher mean curvature function in Euclidean and Minkowski spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:446

Article

de la Fuente, Daniel¹  Romero, Alfonso²  Torres, Pedro J.¹ 

[1] Univ Granada, Dept Matemat Aplicada, E-18071 Granada, Spain

[2] Univ Granada, Dept Geometria & Topol, E-18071 Granada, Spain

关键词: Prescribed higher mean curvature function;    Minkowski spacetime;    Schauder fixed point theorem;    Singular nonlinear equation;   

DOI  :  10.1016/j.jmaa.2016.09.022

来源: Elsevier

【 摘 要 】

In this paper we investigate the existence of rotationally symmetric entire graphs (resp. entire spacelike graphs) with prescribed k-th mean curvature function in Euclidean space Rn+1 (resp. Minkowski spacetime Ln+1). As a previous step, we analyze the associated homogeneous Dirichlet problem on a ball, which is not elliptic for k > 1, and then we prove that it is possible to extend the solutions. Moreover, a sufficient condition for uniqueness is given in both cases. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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