Optimal shapes for positivity preserving
arXiv:2402.16575
Abstract
We are looking for an optimal convex domain on which the boundary value problem $$\left\{\begin{array}{cc}(-Δ)^2 u_γ-γΔu_γ= f,& \mbox{ in }Ω\\ u_γ=\partial_νu_γ=0,& \mbox{ on }\partialΩ\end{array}\right.$$ admits a nonnegative solution for the most , if is a given nonnegative function.