Eigenvalue Homogenization for the p‐Laplacian With Rapidly Oscillating Lq Weights

ABSTRACT In this paper, we study the convergence rates of variational eigenvalues of the ‐Laplacian with rapidly oscillating weights and potentials belonging in a suitable space. Our analysis covers both Dirichlet and Neumann boundary conditions, and we derive explicit estimates in terms of the eigenvalue index and the oscillation parameter . These results are obtained through a detailed examination of certain oscillatory integrals and extend previously known results in the literature.