The behavior of the principal eigenvalue of a mixed elliptic problem with respect to a parameter

In this paper we determine the exact asymptotic behavior of the principal eigenvalue of a mixed elliptic eigenvalue problem which depends on a positive parameter λ when λ → ∞ . We analyze the case in which the problem is considered in a smooth bounded domain Ω of R N , and also the case of planar domains which are smooth except for a finite number of corner points.