The indefinite affine Cauchy problem

DOI10.1016/j.na.2020.111819zbMath1437.53009OpenAlexW3007064344MaRDI QIDQ1988437

Francisco Milán

Publication date: 23 April 2020

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2020.111819

zbMATH Keywords

Cauchy problemaffine maximal surfacesnonlinear fourth-order PDE

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) Affine differential geometry (53A15)

Cites Work

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• The geometric Cauchy problem for the hyperbolic Hessian one equation
• The Björling problem for non-minimal constant mean curvature surfaces
• Björling problem for timelike surfaces in the Lorentz-Minkowski space
• A D'Alembert formula for flat surfaces in the 3-sphere
• On affine-maximal ruled surfaces
• The Bernstein problem for affine maximal hypersurfaces
• Singularities of improper affine maps and their Hessian equation
• The Cauchy problem for indefinite improper affine spheres and their Hessian equation
• The Cauchy problem for the Liouville equation and Bryant surfaces
• The affine Cauchy problem
• Embedded isolated singularities of flat surfaces in hyperbolic 3-space
• The Cauchy problem for improper affine spheres and the Hessian one equation
• Björling problem for maximal surfaces in Lorentz–Minkowski space
• Global affine differential geometry of hypersurfaces
• Affine complete locally convex hypersurfaces

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