14 citations · 66 across the 49 of their papers we have counts for
22 papers · 1 filter
Asymptotic Expansion of the Heat Trace of the Thermoelastic Dirichlet-to-Neumann map
Genqian Liu, Xiaoming Tan
This paper is devoted to study the asymptotic expansion of the heat trace of the Dirichlet-to-Neumann map for the thermoelastic equation on a Riemannian manifold with doundary. By…
The Payne conjecture for Dirichlet and Buckling eigenvalues
Genqian Liu
We prove the long-standing Payne conjecture that the eigenvalue in the buckling problem for a clamped plate is not less than the eigenvalue for…
Spectral Invariants of the Magnetic Dirichlet-to-Neumann Map on Riemannian Manifolds
Genqian Liu, Xiaoming Tan
This paper is devoted to investigate the heat trace asymptotic expansion corresponding to the magnetic Steklov eigenvalue problem on Riemannian manifolds with boundary. We establis…
Determining the viscosity from the boundary information for incompressible fluid
Genqian Liu
For the Stokes equations in a compact connected Riemannian -manifold with smooth boundary , we give an equivalent new system of elliptic equations with $(n+1…
Determining anisotropic real-analytic metric from boundary electromagnetic information
Genqian Liu
For a compact, connected, oriented Riemannian -manifold with smooth boundary , we explicitly give a local representation and a full symbol expression for th…
Determination of isometric real-analytic metric and spectral invariants for elastic Dirichlet-to-Neumann map on Riemannian manifolds
Genqian Liu
In this paper, the elastic Dirichlet-to-Neumann map is studied for the stationary elasticity system in a compact Riemannian manifold with smooth boundary …