论文标题
当$ M $ -CONVEX夹杂物接近矩阵边界时，电场的渐近电场渐近学
Asymptotics for the electric field when $M$-convex inclusions are close to the matrix boundary
论文作者
论文摘要
在复合材料的完美导电性问题中，电场可能会随着$ \ varepsilon $（夹杂物和矩阵边界之间的距离）而变得任意大。本文的主要贡献在于开发一个清晰简洁的程序，以建立在所有维度中具有任意形状的完美导体的边界渐近公式，该公式在[29]中明确表现出了爆炸因子$ q [φ] $的奇异性，该界限是通过挑选$ k $ k $ k $ rolder-k $ os k $ k $ k $ k $ k $ k $ k $ k $ k $ k $。特别是，[27]中至少$ c^{3,1} $所需的夹杂物的平滑度被削弱至$ c^{2，α} $，$ 0 <α<1 $。
In the perfect conductivity problem of composites, the electric field may become arbitrarily large as $\varepsilon$, the distance between the inclusions and the matrix boundary, tends to zero. The main contribution of this paper lies in developing a clear and concise procedure to establish a boundary asymptotic formula of the concentration for perfect conductors with arbitrary shape in all dimensions, which explicitly exhibits the singularities of the blow-up factor $Q[φ]$ introduced in [29] by picking the boundary data $φ$ of $k$-order growth. In particular, the smoothness of inclusions required for at least $C^{3,1}$ in [27] is weakened to $C^{2,α}$, $0<α<1$ here.
