| Abstract: |
| This talk is concerned with the Dirichlet spectrum of elliptic operators with bounded and measurable coefficients. In particular, we consider the problem of minimizing the first eigenvalue over all bounded domains with volume 1. When the operator is the Laplacian, the classical Faber-Krahn Theorem states that all minimizers are balls. In the general case, with no regularity assumptions on the coefficient matrix, we show that open minimizers exist and study the boundary regularity of minimizers. |
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