4 papers · 2 filters
Upper bounds for the ratio of the first two eigenvalues of the Robin Laplacian
Guowei Dai, Yingxin Sun
We sharpen upper bounds for the ratio of the first two Robin eigenvalues by matching the first eigenvalue on a comparison ball with an independently chosen boundary parameter. The…
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} -Δu=μu\,\, &\text{in}\,\, B,\\ \partial_\texttt{n} u+αu=0 &\text{on}\,\, \partial…
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{equation}…