The geometric Cauchy problem for the hyperbolic Hessian one equation
Martínez-López, Antonio
Milán López, Francisco
Cauchy problem
Hyperbolic Hessian one equation
Improper affine spheres
We solve the problem of finding all indefinite improper affine spheres passing through a given regular curve of R3R3 with a prescribed affine co-normal vector field along this curve. We prove the problem is well-posed when the initial data are non-characteristic 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.
2015-09-30T11:31:12Z
2015-09-30T11:31:12Z
2015
info:eu-repo/semantics/article
Martínez-López, A.; Milán López, F. The geometric Cauchy problem for the hyperbolic Hessian one equation. Nonlinear Analysis: Theory, Methods and Applications, 125: 323–333 (2015). [http://hdl.handle.net/10481/37917]
0362-546X
http://hdl.handle.net/10481/37917
10.1016/j.na.2015.05.021
eng
http://creativecommons.org/licenses/by-nc-nd/3.0/
info:eu-repo/semantics/openAccess
Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License