论文标题
三重膜问题中的自由边界规律性
Free boundary regularity in the triple membrane problem
论文作者
论文摘要
我们研究了3个弹性膜问题中自由边界的规律性。 我们表明，对应于连续膜之间巧合区域的两个自由边界为$ c^{1，\ log} $ - 在常规交叉点附近的Hypersurfaces。我们还研究了两种类型的奇异交集。 $ c^{1，α} $ - hypersurface本地覆盖的第一种单数点。第二种类型的单数点分层和每个层面都被$ C^1 $ -Manifold局部覆盖。
We investigate the regularity of the free boundaries in the 3 elastic membranes problem. We show that the two free boundaries corresponding to the coincidence regions between consecutive membranes are $C^{1,\log}$-hypersurfaces near a regular intersection point. We also study two types of singular intersections. The first type of singular points are locally covered by a $C^{1,α}$-hypersurface. The second type of singular points stratify and each stratum is locally covered by a $C^1$-manifold.
