Γ-convergence of Nonlocal Dirichlet Energies With Penalty Formulations of Dirichlet Boundary Data

09/19/2023

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by   Weiye Gan, et al.

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We study nonlocal Dirichlet energies associated with a class of nonlocal diffusion models on a bounded domain subject to the conventional local Dirichlet boundary condition. The Dirichlet boundary condition is imposed through a specifically designed penalty formulation. We prove that the nonlocal Dirichlet energies with the penalty terms converge to local Dirichlet energies with Dirichlet boundary conditions in the sense of -convergence.