The geometric Cauchy problem for the hyperbolic Hessian one equation

被引：2

作者：

Martinez, Antonio ^{[1
]}

Milan, Francisco ^{[1
]}

机构：

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

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2015年 / 125卷

关键词：

Cauchy problem; Hyperbolic Hessian one equation; Improper affine spheres; IMPROPER AFFINE SPHERES; FLAT SURFACES; SINGULARITIES;

D O I：

10.1016/j.na.2015.05.021

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We solve the problem of finding all indefinite improper affine spheres passing through a given regular curve of R-3 with a prescribed affine co-normal vector field along this curve. We prove the problem is well-posed when the initial data are noncharacteristic and show that uniqueness of the solution can fail at characteristic directions. As application we classify the indefinite improper affine spheres admitting a geodesic planar curve. (C) 2015 Elsevier Ltd. All rights reserved.

引用

页码：323 / 333

页数：11

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