On the Uniqueness of Minimal Surface Equation in an Infinite Sector Domainith Capillary Boundary Condition

We consider the minimal surface equation in an infinite sector domain with given capillary boundary conditions.First, we give a necessary and sufficient conditions for the existence of the linear solution. Second, we study the behavior of the solutions of the minimal surface equation at the origin and at the infinite by using the blow up and the sip in process. Finally, we claim that the solution is linear on the boundary and conclude that it is a plane.