Rearrangement inequalities and applications to isoperimetric problems for eigenvalues

@inproceedings{Hamel2006RearrangementIA,
  title={Rearrangement inequalities and applications to isoperimetric problems for eigenvalues},
  author={François Hamel and Nikolai S. Nadirashvili and Emmanuel Russ},
  year={2006}
}
Let Ω be a bounded C2 domain in Rn, where n is any positive integer, and let Ω∗ be the Euclidean ball centered at 0 and having the same Lebesgue measure as Ω. Consider the operator L = −div(A∇) + v · ∇ + V on Ω with Dirichlet boundary condition, where the symmetric matrix field A is in W 1,∞(Ω), the vector field v is in L∞(Ω, Rn) and V is a continuous function in Ω. We prove that minimizing the principal eigenvalue of L when the Lebesgue measure of Ω is fixed and when A, v and V vary under some… CONTINUE READING