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Correctness of the definition of the Laplace operator with delta-like potentials
Complex Variables and Elliptic Equations ( IF 0.6 ) Pub Date : 2020-12-15 , DOI: 10.1080/17476933.2020.1849164
B. E. Kanguzhin 1 , K. S. Tulenov 1, 2
Affiliation  

ABSTRACT

In this paper, we give a correct definition of the Laplace operator with delta-like potentials. Correctly solvable pointwise perturbation is investigated and formulas of resolvent are described. We study some properties of the resolvent. In particular, we prove Krein's formula for these resolvents.



中文翻译:

具有类 delta 势的拉普拉斯算子定义的正确性

摘要

在本文中,我们给出了具有类 delta 势的拉普拉斯算子的正确定义。研究了可正确求解的逐点微扰,并描述了求解公式。我们研究了溶剂的一些性质。特别是,我们证明了这些解决方案的 Krein 公式。

更新日期:2020-12-15
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