We consider a biharmonic problem Δ²u_ω = f_ω with Navier type boundary conditions u_ω = Δu_ω = 0, on a family of truncated sectors Ω_ω in ℝ² of radius r, 0 < r < 1 and opening angle ω, ω ∈ (2π/3, π] when ω is close to π. The family of right-hand sides (f_ω)_ω∈(2π/3, π] is assumed to depend smoothly on ω in L²(Ω_ω). The main result is that u_ω converges to u_π when ω → π with respect to the H²-norm. We can also show that the H²-topology is optimal for such a convergence result.

中文翻译：

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截断的凸扇区上在角度π附近的双调和问题解的H 2收敛性

我们考虑一个双调和问题Δ ² Ù _ω = ˚F _ω与纳维型边界条件Ù _ω =Δ Ù _ω = 0时，对一个家庭截断扇区Ω _ω在ℝ ²半径的[R，0 < - [R <1和张角ω ，ω＆Element;（2π/ 3，π]当ω接近于π。右手边的家族（˚F _ω）_ω＆Element;（2π/ 3，π]被假定为上顺利依赖ω在大号²（Ω _ω），主要结果是，ü _ω收敛于û _π当ω →交通π相对于所述ħ ²范数。我们还可以证明，H ^2-拓扑对于这种收敛结果是最佳的。