Abstract
We investigate for which range of b the biharmonic boundary value problem Δ 2 u + bu = f in Q, with Δu = u = 0 on ∂Ω, is positivity-preserving in the sense that f ≥ 0 in Ω implies u ≥ 0. We will also disprove a conjecture of McKenna and Walter on the isoperimetric nature of the upper bound be (Ω) for such b. The investigation gives rise to related questions for certain linear elliptic systems and to curious identities for sums of inverse eigenvalues.
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