On Principal Eigenvalues for Periodic Parabolic Problems with Optimal Condition on the Weight Function1

Let be a bounded domain in N and let m be a T-periodic function such that its restriction to × 0 T belongs to Ls 0 T Lv for some v > N 2 and s > 2v 2v−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.