LAUSR

Abstract We consider a smooth solution u > 0 of the singular minimal surface equation 1 + | D u | 2  div ( D u / 1 + | D u | 2 ) = α / u defined in a bounded strictly convex domain of R 2 with constant boundary condition. If α 0 , we prove the existence a unique critical point of u. We also derive some C 0 and C 1 estimates of u by using the theory of maximum principles of Payne and Philippin for a certain family of Φ-functions. Finally we deduce an existence theorem of the Dirichlet problem when α 0 .