在這篇論文裡，我們使用形式inf∫Ω {(ε/2)k|▽u|^2+(1/4ε)(a-u)^2(b+u)^2}dx對於變異問題建構一個局部低點，這裡ε是一個很小的正參數且Ω⊂R^n是一個平滑有邊界的凸有界定義域。其中k∈C3(Ω)是在定義域Ω的閉包中的嚴格正函數。如果我們在所有函數H^1(Ω)中取最大下界，我們就會得到符合Neumann 邊界條件偏微分方程的正數解。
我們希望限制最大下界於局部低點，因此我們考慮這Neumann問題的解在Ω上取所有正負號的值且讓它們等於零的值在(n-1)超維度表面Гε⊂Ω。藉由Г收斂法，我們從定義域Ω上的權重測線可以發現當ε→0的極限解的結構。

In this thesis,we construct local minima of a certain variational problem which we take in the form inf∫Ω {(ε/2)k|▽u|^2+(1/4ε)(a-u)^2(b+u)^2}dx, where ε is a small positive parameter and Ω⊂R^n is a convex bounded domain with smooth boundary. Here k∈C3(Ω) is strictly positive functions in the closure of the domain Ω. If we take the inf over all functions H^1(Ω), we obtain the positive solution of the partial differential equation with Neumann boundary conditions.
We wish to restrict the inf to local (not global) minima so that we consider solutions of this Neumann problem which take both signs in and which vanish on (n-1) dimensional
hypersurfaces Гε⊂Ω. By using a Г-convergence method, we nd the structure of the limit solutions as ε→0 in terms of the weighted geodesics of the domain Ω.

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