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

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• 作者：Daniel de la Fuente^a ; ^{delafuente@ugr.es" class="auth_mail" title="E-mail the corresponding author} ; Alfonso Romero^b ; ^{aromero@ugr.es" class="auth_mail" title="E-mail the corresponding author} ; Pedro J. Torres^a ; ^{ptorres@ugr.es" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Prescribed higher mean curvature function ; Minkowski spacetime ; Schauder fixed point theorem ; Singular nonlinear equation
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 February 2017
• 年：2017
• 卷：446
• 期：1
• 页码：1046-1059
• 全文大小：394 K

文摘

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${\mathbb{R}}^{n+1}$ (resp. Minkowski spacetime Lⁿ⁺¹${\mathbb{L}}^{n+1}$). As a previous step, we analyze the associated homogeneous Dirichlet problem on a ball, which is not elliptic for k>1$k>1$, and then we prove that it is possible to extend the solutions. Moreover, a sufficient condition for uniqueness is given in both cases.