论文标题
非本地竞争术语的光谱形状优化问题
A spectral shape optimization problem with a nonlocal competing term
论文作者
论文摘要
我们研究了将光谱功能的最小化作为Dirichlet Laplacian的第一个特征值和Riesz型相互作用功能的相对强度的最小化。我们表明，当Riesz排斥强度低于临界价值时，就会发生最小化器的存在。然后，我们通过扩展分析证明，当Riesz排斥足够小时，球是一个刚性的最小化器。最终，我们表明，对于Riesz排斥的某些制度，不存在常规的最小化器。
We study the minimization of a spectral functional made as the sum of the first eigenvalue of the Dirichlet Laplacian and the relative strength of a Riesz-type interaction functional. We show that when the Riesz repulsion strength is below a critical value, existence of minimizers occurs. Then we prove, by means of an expansion analysis, that the ball is a rigid minimizer when the Riesz repulsion is small enough. Eventually we show that for certain regimes of the Riesz repulsion, regular minimizers do not exist.
