On the fine structure of the solutions to nonlinear thin two-membrane
problems in 2D
On the fine structure of the solutions to nonlinear thin two-membrane
problems in 2D
We prove a structure theorem for the solutions of nonlinear thin two-membrane problems in dimension two. Using the theory of quasi-conformal maps, we show that the difference of the sheets is topologically equivalent to a solution of the linear thin obstacle problem, thus inheriting its free boundary structure. More precisely, …