Outputs (2)

Upper bounds for Steklov eigenvalues of submanifolds in Euclidean space via the intersection index (2021)
Journal Article
Colbois, B., & Gittins, K. (2021). Upper bounds for Steklov eigenvalues of submanifolds in Euclidean space via the intersection index. Differential Geometry and its Applications, 78, Article 101777. https://doi.org/10.1016/j.difgeo.2021.101777

We obtain upper bounds for the Steklov eigenvalues σk(M)of a smooth, compact, n-dimensional submanifold M of Euclidean space with boundary Σ that involve the intersection indices of M and of Σ. One of our main results is an explicit upper bound in te... Read More about Upper bounds for Steklov eigenvalues of submanifolds in Euclidean space via the intersection index.

Courant-sharp Robin eigenvalues for the square: The case of negative Robin parameter (2021)
Journal Article
Gittins, K., & Helffer, B. (2021). Courant-sharp Robin eigenvalues for the square: The case of negative Robin parameter. Asymptotic Analysis, 124(1-2), 69-107. https://doi.org/10.3233/asy-201642

We consider the cases where there is equality in Courant’s nodal domain theorem for the Laplacian with a Robin boundary condition on the square. In our previous two papers, we treated the cases where the Robin parameter h>0 is large, small respective... Read More about Courant-sharp Robin eigenvalues for the square: The case of negative Robin parameter.