We are looking for an optimal convex domain on which the boundary value problem (-Δ)² u_γ-γΔ u_γ = f,& in Ω\\ u_γ=∂_ν u_γ=0,& on ∂Ωarray. admits a nonnegative solution for the most γ, if f is a given nonnegative function.
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Sascha Eichmann (2024) studied this question.
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