Convergence Analysis of Singular Perturbation for a Class of Double Phase Obstacle Inclusions

We focus primarily on the convergence analysis of singular perturbation for a class of double phase obstacle inclusions with mixed boundary conditions and two set-valued terms defined respectively in the domain $ \Omega $ and on the boundary $ \partial\Omega_{2} $ . More precisely, we introduce a family of singular perturbation problems corresponding to the double phase obstacle inclusion under consideration. Then we prove the existence of solutions to the singular perturbation problems. Finally, a convergence theorem is established which shows that the solution set of the double phase inclusion can be approximated by the solution set of the singular perturbation problem in the Kuratowski sense.