7 papers · 1 filter
A priori Dirichlet energy bounds for positive Trudinger--Moser critical points on simply connected planar domains
Hongtao Hu, Qiaoran Wu, Wenming Zou
\noindent Let \(\Om\subset\R^2\) be a smooth bounded simply connected domain. We prove that all positive solutions of \(-Δu=θue^{u^2}\), with \(θ>0\) and zero Dirichlet boundary da…
Sharp higher-order uncertainty principles
Hongtao Hu, Meiqi Liu, Wenming Zou
We establish a class of sharp higher-order inequalities related to the uncertainty principle. First, by means of the expanding the squares method, we give a concise proof of sharp…
Sharp Harmonic-Mean Bounds for Neumann Eigenvalues on Riemannian Surfaces and Counterexamples to Geodesic Ball Optimality on Higher-Dimensional Spheres
Hongtao Hu, Meiqi Liu, Qiaoran Wu +1
Let be a bounded simply connected Lipschitz domain with conformal metric , where is positive in the interior and may te…
A sharp two-disk bound for the second positive Neumann eigenvalue under a curvature upper bound
Meiqi Liu, Zhouyu Long, Wenming Zou
We prove the sharp two-disk comparison conjectured by Langford and Laugesen for the second positive Neumann eigenvalue under an upper Gaussian-curvature bound, and strengthen it to…
Cumulative angular cancellation in Maz'ya's endpoint inequalities
Zhouyu Long, Wenming Zou
We establish domain criteria for critical homogeneous potential inequalities in the plane. Assuming signed plane cancellation, uniform absolute summability of frozen annular moment…
Uniqueness of bound states to the logarithmic Schrödinger equation
Tianhao Liu, Xin Sun, Wenming Zou
This paper studies the uniqueness of bound states for the problem Δu + u\log u ^2=0, \quad u\in H^1(\RN), \quad n\geq 2, which arises from the logarithmic Schrödinger equation. We…
Sharp quantitative stability for the fractional Sobolev trace inequality
Yingfang Zhang, Yuxuan Zhou, Wenming Zou
In this paper, we study the stability of fractional Sobolev trace inequality within both the functional and critical point settings. In the functional setting, we establish the fol…