Some isoperimetric problems for the principal eigenvalues of second-order elliptic operators in divergence form

Abstract

We prove various optimization results for the principal eigenvalues of general second-order elliptic operators in divergence form with Dirichlet boundary condition in C 2 bounded nonempty domains of R n . In particular, we obtain a ‘Faber–Krahn’ type inequality for these operators. The proofs use a new rearrangement technique. To cite this article: F. Hamel et al., C. R. Acad. Sci. Paris, Ser. I 344 (2007).