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Upper bounds for Steklov eigenvalues of submanifolds in Euclidean space via the intersection index
Bruno Colbois, Katie Gittins
We obtain upper bounds for the Steklov eigenvalues of a smooth, compact, connected, -dimensional submanifold of Euclidean space with boundary that involve the i…
Courant-sharp Robin eigenvalues for the square: the case of negative Robin parameter
Katie Gittins, Bernard Helffer
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 trea…
Courant-sharp Robin eigenvalues for the square -- the case with small Robin parameter--
Katie Gittins, Bernard Helffer
This article is the continuation of our first work on the determination of the cases where there is equality in Courant's Nodal Domain theorem in the case of a Robin boundary condi…
Courant-sharp Robin eigenvalues for the square and other planar domains
Katie Gittins, Bernard Helffer
This paper is devoted to the determination of the cases where there is equality in Courant's nodal domain theorem in the case of a Robin boundary condition. For the square, we part…
Steklov eigenvalues of submanifolds with prescribed boundary in Euclidean space
Bruno Colbois, Alexandre Girouard, Katie Gittins
We obtain upper and lower bounds for Steklov eigenvalues of submanifolds with prescribed boundary in Euclidean space. A very general upper bound is proved, which depends only on th…