Optimizing the first eigenvalue of some quasilinear operators with respect to the boundary conditions

We consider a class of quasilinear operators on a bounded domain $Ω\subset \mathbb R^n$ and address the question of optimizing the first eigenvalue with respect to the boundary conditions, which are of the Robin-type. We describe the optimizing boundary conditions and establish upper and lower bounds on the respective maximal and minimal eigenvalue.

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