6 citations · 19 across the 11 of their papers we have counts for
5 papers · 1 filter
Compactness and sharp lower bound for a 2D smectics model
Michael Novack, Xiaodong Yan
We consider a 2D smectics model \begin{equation*} E_{ε}\left( u\right) =\frac{1}{2}\int_Ω\frac{1}{\varepsilon }\left( u_{z}-\frac{1% }{2}u_{x}^{2}\right) ^{2}+\varepsilon \left( u_…
The Brezis-Nirenberg problem for fractional elliptic operators
Ko-Shin Chen, Marcos Montenegro, Xiaodong Yan
In the present paper, we study the effect of an elliptic operator in divergence form L defined in a bounded open set on the existence and nonexistence of positive solutions of the…
Uniqueness of one-dimensional Néel wall profiles
Cyrill B. Muratov, Xiaodong Yan
We study the domain wall structure in thin uniaxial ferromagnetic films in the presence of an in-plane applied external field in the direction normal to the easy axis. Using the re…
An integral equation in conformal geometry
Fengbo Hang, Xiaodong Wang, Xiaodong Yan
We study the existence of a metric with zero scalar curvature maximizing the isoperimetric ratio among all zero scalar curvature metrics in a fixed conformal class of metrics on a…
Sharp integral inequalities for harmonic functions
Fengbo Hang, Xiaodong Wang, Xiaodong Yan
Motivared by Carleman's proof of the isoperimetric inequality in the plane, we study some sharp integral inequalities for harmonic functions on the upper halfspace. We also derive…