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math.AP2025
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…
math.AP2025
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…
math.AP2025
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…