On the behavior of a non-parametric minimal surface in a non-convex quadrilateral
The boundary behaviour of generalized solutions of the Dirichlet problem for the minimal surface equation is studied. In particular the special case of a nonconvex quadrilateral is considered by the authors. In this case the only point of interest is the behaviour of the solution at the reentrant corner of the domain. It is known since some time, that for special senseful boundary values a classical solution of the boundary value problem does not exist. But weak solutions in the usual setting exist. It is shown that the generalized solution may be thought as the solution of an obstacle problem.
scientific article; zbMATH DE number 4005029
scientific article