(untitled) (Analysis in Theory and Applications, 2021)
Let Ω, with finite Lebesgue measure |Ω|, be a non-empty open subset of R, and Ω=_j=1^∞Ω_j, where the open sets Ω_j are pairwise disjoint and the boundary Γ=Ω has Minkowski dimension D(0,1). In this paper we study the Dirichlet eigenvalues problem on the domain Ω and give the exact second asymptotic term for the eigenvalues, which is related to the Minkowski dimension D. Meanwhile, we give sharp lower bound estimates for Dirichlet eigenvalues for such one-dimensional fractal domains.