4 papers
Upper bound estimation for the ratio of the first two eigenvalues of Robin Laplacian
Guowei Dai, Yingxin Sun
The celebrated conjecture by Payne, Pólya and Weinberger (1956) states that for the fixed membrane problem, the ratio of the first two eigenvalues, , is maximized by a…
Complete spectrum of the Robin eigenvalue problem on the ball
Guowei Dai, Yingxin Sun
We investigate the following Robin eigenvalue problem \begin{equation*} \left\{ \begin{array}{ll} -Îu=μu\,\, &\text{in}\,\, B,\\ \partial_\texttt{n} u+αu=0 &\text{on}\,\, \parti…
On the Schiffer and Berenstein conjectures with high-frequency for convex domains in the plane
Guowei Dai, Yingxin Sun, Juncheng Wei +1
In this paper, by introducing two-point stationary-phase amplitude defect, we provide a partial positive answer to the Schiffer and Berenstein conjectures in . More p…
Confirmed answer to the Schiffer conjecture and the Berenstein conjecture
Guowei Dai
Let be a bounded domain in with a connected () boundary. We show that, if the following overdetermined elliptic problem \begin{equati…