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We prove the existence of a unique viscosity solution to certain systems offully nonlinear parabolic partial differential equations with interconnectedobstacles in the setting of Neumann boundary conditions. The method of proofbuilds on the classical viscosity solution technique adapted to the setting ofinterconnected obstacles and construction of explicit viscosity sub- andsupersolutions as bounds for Perron's method. Our motivation stems from socalled optimal switching problems on bounded domains.

Systems of fully nonlinear parabolic obstacle problems with Neumann boundary conditions