Sum of the negative eigenvalues for the semi-classical Robin Laplacian

We compute the sum of the negative eigenvalues of a semi-classical version of the Robin Laplace operator. This version of the operator arises naturally from the Laplace operator with a Robin boundary condition and a strong coupling parameter. Viewing the operator from the ‘semi-classical’ angle has...

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Bibliographic Details
Published in:Revista matemática complutense 2020-09, Vol.33 (3), p.767-795
Main Authors: Kachmar, Ayman, Nasrallah, Marwa
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Boundary conditions
Eigenvalues
Geometry
Laplace transforms
Mathematics
Mathematics and Statistics
Topology
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Summary:We compute the sum of the negative eigenvalues of a semi-classical version of the Robin Laplace operator. This version of the operator arises naturally from the Laplace operator with a Robin boundary condition and a strong coupling parameter. Viewing the operator from the ‘semi-classical’ angle has allowed for many non-trivial results. In the same vein, this contribution is no exception with the main significance being that the function in the boundary condition satisfies minimal regularity assumptions. Earlier contributions were devoted to the case when the function in the boundary condition is constant.
ISSN:1139-1138
1988-2807
DOI:10.1007/s13163-019-00338-7