(untitled) (Journal of Partial Differential Equations, 2020)
Let ΩR^4 be a smooth bounded domain, W_0^2,2(Ω) be the usual Sobolev space. For any positive integer , λ_(Ω) is the -th eigenvalue of the bi-Laplacian operator. Define E_=E_λ_1(Ω)E_λ_2(Ω)…E_λ_(Ω), where E_λ_i(Ω) is eigenfunction space associated with λ_i(Ω). E^_ denotes the orthogonal complement of E_ in W_0^2,2(Ω). For 0≤α