Liouville Theorems for a Class of Degenerate or Singular Monge–Ampère Equations
摘要
In this note, we classify solutions to a class of Monge–Ampère equations whose right hand side may be degenerate or singular in the half space. Solutions to these equations are special solutions to a class of fourth order equations, including the affine maximal hypersurface equation, in the half space. Both the Dirichlet boundary value and Neumann boundary value cases are considered.