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- W2052002682 abstract "We study the problem of positivity preserving of the Green operator for the polyharmonic operator (−Δ) m under homogeneous Dirichlet boundary conditions on domains Ω of ℝR 2. Here we will treat only Ω, which are ε-close to a disk B in C m,γ-sense, meaning, there exists a C m,γ-mapping g : $$ bar{B}longrightarrow bar{Omega}$$ such that g⊼(B) = ⊼Ω and $$||g -- Id||_{C^{m,gamma}}(bar{B})!leq!varepsilon$$ . We show that ε-closeness in C m, γ-sense is enough in order to ensure positivity preserving. For the clamped plate equation (i.e. m = 2), this means that it is a Hölder norm of the curvature of ∂ Ω, which governs the positivity behavior. This improves the previous work by Grunau and Sweers, where closeness to the disk in C 2m -sensewas required (in C 4-sense for thethe clamped plate)." @default.
- W2052002682 created "2016-06-24" @default.
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- W2052002682 date "2006-03-17" @default.
- W2052002682 modified "2023-10-05" @default.
- W2052002682 title "Positivity for polyharmonic problems on domains close to a disk" @default.
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- W2052002682 doi "https://doi.org/10.1007/s10231-006-0012-3" @default.
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