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math.AP2024
Optimal shapes for positivity preserving
Sascha Eichmann
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 }\par…
math.AP2024
Improved long time existence for the Willmore flow of surfaces of revolution with Dirichlet data
Sascha Eichmann
To avoid possible singularities in the Willmore flow, one usually works under an energy threshold provided by the Li-Yau inequality. Here we improve this threshold by also consider…