17 citations · 154 across the 69 of their papers we have counts for
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Sharp Well-posedness for the Benjamin Equation
Wengu Chen, Zihua Guo, Jie Xiao
Having the ill-posedness in the range of the Cauchy problem for the Benjamin equation with an initial data, we prove that the already-established loca…
A Sharp Bilinear Estimate for the Bourgain-type Space with Application to the Benjamin Equation
Wengu Chen, Jie Xiao
This note shows the existence of a sharp bilinear estimate for the Bourgain-type space and gives its application to the optimal local well/ill-posedness of the Cauchy problem for t…
Coarse and Precise -Green Potential Estimates on Noncompact Riemannian Manifolds
Jie Xiao
We are concerned about the coarse and precise aspects of a priori estimates for Green's function of a regular domain for the Laplacian-Betrami operator on any -dimensional…
An Asymmetric Affine Pólya--Szegö Principle
Christoph Haberl, Franz E. Schuster, Jie Xiao
An affine rearrangement inequality is established which strengthens and implies the recently obtained affine Pólya--Szegö symmetrization principle for functions on .…
The double Ringel-Hall algebra on a hereditary abelian finitary length category
Rujing Dou, Qunhua Liu, Jie Xiao
In this paper, we study the category of semi-stable coherent sheaves of a fixed slope over a weighted projective curve. This category has nice properties: i…
The -Faber-Krahn Inequality Noted
Jie Xiao
When revisiting the Faber-Krahn inequality for the principal -Laplacian eigenvalue of a bounded open set in with smooth boundary, we simply rename it as the -Fa…