ON A VOLUME CONSTRAINED FOR THE FIRST EIGENVALUE OF THE P-LAPLACIAN OPERATOR
Idrissa Ly, Abdus Salam · 2009
In this paper, we are interested in a shape optimization problem which consists in minimizing the functional that associates to an open set the first eigenvalue for p-Laplacian operator with homogeneous boundary condition. The minimum is taken among all open subsets with prescribed measure of a given bounded domain. We study an existence result for the associate variational problem. Our technique consists in enlarging the class of admissible functions to the whole space W 1,p 0 (D), penalizing those functions whose level sets have a measure which is less than those required. In fact, we study the minimizers of a family of penalized functionals Jλ, λ > 0 � −�