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 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.