Estimates for the first eigenvalue for p-Laplacian with mixed boundary conditions
Kui Wang · Journal of Mathematical Inequalities · 2018
In this article, we consider eigenvalue problems on domains with an interior hole. Precisely, we show a Cheng-type inequality on manifolds, and certain Faber-Krahn inequalities on space forms. Besides, we obtain upper and lower bounds of the eigenvalue through the classic Dirchlet eigenvalue, implying convergence of the eigenvalue as the hole tends to / 0 .