Mathematics – Analysis of PDEs
Scientific paper
2009-12-20
Mathematics
Analysis of PDEs
42 pages
Scientific paper
Let $\Omega$ be a bounded domain with $C^2$-smooth boundary in an $n$-dimensional oriented Riemannian manifold. It is well-known that for the bi-harmonic equation $\Delta^2 u=0$ in $\Omega$ with the $0$-Dirichlet boundary condition, there exists an infinite set $\{u_k\}$ of biharmonic functions in $\Omega$ with positive eigenvalues $\{\lambda_k\}$ satisfying $\Delta u_k+ \lambda_k \varrho \frac{\partial u_k}{\partial \nu}=0$ on the boundary $\partial \Omega$. In this paper, by a new method we establish the Weyl-type asymptotic formula for the counting function of the biharmonic Stekloff eigenvalues $\lambda_k$.
No associations
LandOfFree
The Weyl-type asymptotic formula for biharmonic Steklov eigenvalues with Dirichlet boundary condition on Riemannian manifolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The Weyl-type asymptotic formula for biharmonic Steklov eigenvalues with Dirichlet boundary condition on Riemannian manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Weyl-type asymptotic formula for biharmonic Steklov eigenvalues with Dirichlet boundary condition on Riemannian manifolds will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-62327