Existence and Convergence Results for the Galerkin Approximation of an Electronic Density Functional

We formulate and analyze a model for the study of finite clusters of atoms or localized defects in infinite crystals based on orbital-free density functional theory. We show that the resulting constrained optimization problem has a minimizer and we provide a careful analysis of the solvability of the associated Euler–Lagrange equation. Based on these results, and using tools from saddle-point theory and nonlinear analysis, we then show that a Galerkin discretization has a solution that converges to the correct limit.

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