We consider the laplacian in a domain squeezed between two parallel curves in the plane, subject to Dirichlet boundary conditions on one of the curves and Neumann boundary conditions on the other. We derive two-term asymptotics for eigenvalues in the limit when the distance between the curves tends to zero. The asymptotics are uniform and local in the sense that the coefficients depend only on the extremal points where the ratio of the curvature radii of the Neumann boundary to the Dirichlet one...
We consider the Laplacian in a domain squeezed between two parallel hypersurfaces in Euclidean spaces of any dimension, subject to Dirichlet boundary conditions on one of the hypersurfaces and Neumann boundary conditions on the other. We derive two-term asymptotics for eigenvalues in the limit when the distance between the hypersurfaces tends to zero. The asymptotics are uniform and local in the sense that the coefficients depend only on the extremal points where the ratio of the area of the Neumann...
We consider the Laplacian in a domain squeezed
between two parallel curves in the plane,
subject to Dirichlet boundary conditions on one of the curves
and Neumann boundary conditions on the other.
We derive two-term asymptotics for eigenvalues
in the limit when the distance between the curves tends to zero.
The asymptotics are uniform and local in the sense that
the coefficients depend only on the extremal points where
the ratio of the curvature radii of the Neumann boundary
to the Dirichlet one...
Download Results (CSV)