伪相对论能量局域化的Sobolev不等式

Existence of optimizers in a Sobolev inequality for vector fields

We consider the minimization problem corresponding to a Sobolev inequality for vector fields and show that minimizing sequences are relatively compact up to the symmetries of the problem. In particular, there is a minimizer. An ingredient in our proof is a version of the Rellich--Kondrachov compactness theorem for sequences satisfying a nonlinear constraint.

近临界Ising模型的对数Sobolev不等式

Log-Sobolev inequality for near critical Ising models

对于一般铁磁Ising模型，证明了对数Sobolev常数可用磁化率表示的简单界，使其在直至临界点时与系统大小一致，并在均场条件下多项式依赖于到临界点的距离和体积。