论文标题
Laplacians具有混合边界条件的Laplacians最低特征值之间的不平等
Inequalities between the lowest eigenvalues of Laplacians with mixed boundary conditions
论文作者
论文摘要
考虑到具有混合边界条件的有界，平面，凸形域上拉普拉斯的特征值问题，其中将迪利奇的边界条件施加在边界的一部分上，而诺伊曼边界条件的补充。鉴于两个不同的边界条件选择相同域的选择，我们证明其最低特征值之间的不平等现象。作为一种特殊情况，我们证明了三角形混合特征值的猜想的一部分。
The eigenvalue problem for the Laplacian on bounded, planar, convex domains with mixed boundary conditions is considered, where a Dirichlet boundary condition is imposed on a part of the boundary and a Neumann boundary condition on its complement. Given two different such choices of boundary conditions for the same domain, we prove inequalities between their lowest eigenvalues. As a special case, we prove parts of a conjecture on the order of mixed eigenvalues of triangles.
