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The Discrete Dirichlet Problem

Mathematical Physics & Probability

Speaker: Daniel Ueltschi, UC Davis
Location: 693 Kerr
Start time: Tue, Oct 23 2001, 4:10PM

The sum of N lowest eigenvalues of the discrete Laplace operator in an arbitrary domain D, with Dirichlet boundary conditions, represents the ground state energy of N electrons in D. Inspired by a work of P. Li and S.-T. Yau for the analogous operator in the continuum, which proves that this sum is bounded below by its `bulk term', we can show that this sum goes like the bulk term plus a positive term that is proportional to the boundary of the domain.