Elliptic equations in divergence form, geometric critical points of solutions, and Stekloff eigenfunctions
Elliptic equations in divergence form, geometric critical points of solutions, and Stekloff eigenfunctions
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DOI：
10.1137/s0036141093249080
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发表时间：
1994-09
影响因子：
2
通讯作者：
G. Alessandrini;R. Magnanini
中科院分区：
文献类型：
--
作者：
G. Alessandrini;R. Magnanini
Stekloff本征值问题（1.1）具有可计数的本征值$\{ p_n \} n = 1，2，\ldots $，每个本征值都有有限重数。本文给出了p_n $的重数、临界点个数和节点域个数的一个整数n的上估计.考虑到p_n $在电导率反问题中的可能应用，对于一般情况的具有间断系数的散度型椭圆型方程，通过替换经典的临界点与更合适的几何临界点的概念。
The Stekloff eigenvalue problem (1.1) has a countable number of eigenvalues $\{ p_n \} n = 1,2, \ldots $, each of finite multiplicity. In this paper the authors give an upper estimate, in terms of the integer n, of the multiplicity of $p_n $, and the number of critical points and of nodal domains of the eigenfunctions corresponding to $p_n $.In view of a possible application to inverse conductivity problems, the result for the general case of elliptic equations with discontinuous coefficients in divergence form is proven by replacing the classical concept of critical point with the more suitable notion of geometric critical point.