On Principal Eigenvalues for Periodic Parabolic Problems with Optimal Condition on the Weight Function

AbstractLet Ω be a bounded domain in RN and let m be a T-periodic function such that its restriction to Ω×(0,T) belongs to Ls((0,T),Lv(Ω)) for some v>N2 and s>2v2v−N, with v>1 and s≥2. We give necessary and sufficient conditions on m for the existence, uniqueness, and simplicity of the principal eigenvalue for the Dirichlet periodic parabolic eigenvalue problem with weight m