4 citations · 5 across the 9 of their papers we have counts for
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Optimisation of Steklov transmission eigenvalues and minimal surfaces
Mikhail Karpukhin, Alain Didier Noutchegueme
In the present paper, we study the variational properties of Steklov transmission eigenvalues, which can be seen as eigenvalues of the sum of two Dirichlet-to-Neumann operators on…
Second Variation Formula for Eigenvalue Functionals on Surfaces
Mikhail Karpukhin
Consider the first nontrivial eigenvalue of the Laplacian on a closed surface as a functional on the space of Riemannian metrics of unit area. N. Nadirashvili has discovered a rema…
Flexibility of Steklov eigenvalues via boundary homogenisation
Mikhail Karpukhin, Jean Lagacé
Recently, D. Bucur and M. Nahon used boundary homogenisation to show the remarkable flexibility of Steklov eigenvalues of planar domains. In the present paper we extend their resul…
Weyl's law for the Steklov problem on surfaces with rough boundary
Mikhail Karpukhin, Jean Lagacé, Iosif Polterovich
The validity of Weyl's law for the Steklov problem on domains with Lipschitz boundaries is a well-known open question in spectral geometry. We answer this question in two dimension…
The Dirichlet-to-Neumann map, the boundary Laplacian, and Hörmander's rediscovered manuscript
Alexandre Girouard, Mikhail Karpukhin, Michael Levitin +1
How close is the Dirichlet-to-Neumann (DtN) map to the square root of the corresponding boundary Laplacian? This question has been actively investigated in recent years. Somewhat s…
Continuity of eigenvalues and shape optimisation for Laplace and Steklov problems
Alexandre Girouard, Mikhail Karpukhin, Jean Lagacé
We associate a sequence of variational eigenvalues to any Radon measure on a compact Riemannian manifold. For particular choices of measures, we recover the Laplace, Steklov and ot…
Steklov problem on differential forms
Mikhail Karpukhin
In this paper we study spectral properties of Dirichlet-to-Neumann map on differential forms obtained by a slight modification of the definition due to Belishev and Sharafutdinov.…