Isoperimetric cones and minimal solutions of partial overdetermined problems

In this paper we consider a partial overdetermined mixed boundary value problem in domains inside cone as [18]. We show that, cones having an isoperimetric property, the only which admit solution and minimize torsional energy functional are spherical sectors centered at vertex of cone. also that close C1,1 -metric to one isoperimetric, generalizing so result [1]. This is achieved by using characterization constant mean curvature polar graphs improves