Electronic Journal of Differential Equations,
Vol. 2000(2000), No. 36, pp. 1-10.

Title: Global minimizing domains for the first eigenvalue of an elliptic 
       operator with non-constant coefficients

Authors: Dorin Bucur (Univ. de Franche-Comte, France)
  Nicolas Varchon (Univ. de Franche-Comte, France)
         
Abstract: 
 We consider an elliptic operator, in divergence form, that is a
 uniformly elliptic matrix. We describe the behavior of every  sequence
 of domains which minimizes the first Dirichlet eigenvalue over a
 family of fixed measure domains of $R^N$. 
 The existence of minimizers is proved in some particular situations, 
 for example when the operator is periodic. 

Submitted February 1-st, 2000. Published May 16, 2000.
Math Subject Classifications: 49Q10, 49R50.
Key Words: First eigenvalue;  Dirichlet boundary; non-constant coeffcients;
           optimal domain.