The indefinite affine Cauchy problem. (July 2020)

• Record Type: Journal Article
• Authors: Milán, Francisco
• Is Part Of: Nonlinear analysis. Volume 196(2020)
• Publication Date: 2020-07
• Subjects: 53A15; Cauchy problem -- Nonlinear fourth order PDE -- Affine maximal surfaces; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2020.111819
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We solve the geometric Cauchy problem for the class of affine maximal surfaces, with indefinite affine metric, in the affine space R 3, that is, we find all the surfaces of this class which contain a given regular curve of R 3 with prescribed affine normal and affine conormal along it. 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 (asymptotic) directions. As application we obtain some results about geodesics and symmetries of indefinite affine maximal surfaces.