Uniform local Lipschitz continuity of eigenvalues with respect to the potential in $L^1[a,b]$

关于欧几里得平面中方向Lipschitz连续性的一则注记

A note on directional Lipschitz continuity in the Euclidean plane

该研究针对2017年J. M. Ash与S. Catoiu论文中关于欧几里得平面Lipschitz性质与可微性关系的猜想，证明了其更强形式，并改进了原论文的主要结果。

Optimal parameters related with continuity properties of the multilinear fractional integral operator between Lebesgue and Lipschitz spaces

We deal with the boundedness of the multilinear fractional integral operator $I_{γ,m}$ from a product of weighted Lebesgue spaces into adequate weighted Lipschitz spaces. Our results generalize some previous estimates not only for the linear case but also for the unweighted problem in the multilinear context. We characterize the classes of weights for which the problem described above holds and show the optimal range of the parameters involved. The optimality is understood in the sense that the parameters defining the corresponding spaces belong to a certain region. We further exhibit examples…

Lipschitz and Fourier type conditions with moduli of continuity in rank 1 symmetric spaces

Sufficient and necessary results have been proven on Lipschitz type integral conditions and bounds of its Fourier transform for an $L^2$ function, in the setting of Riemannian symmetric spaces of rank $1$ whose growth depends on a $k$th-order modulus of continuity.

分支粗糙微分方程解的Lipschitz连续性

The Lipschitz continuity of the solution to branched rough differential equations

本文利用Grossman Larson Hopf代数与张量Hopf代数的同构，将次黎曼几何技术用于分支粗糙微分方程，证明了解对初值、向量场和驱动粗糙路径的显式Lipschitz连续性。

用Lipschitz函数捕捉度量值映射的跳跃

Catching jumps of metric-valued mappings with Lipschitz functions

本文研究了度量值映射的跳跃捕捉问题，证明了连续性假设在特征化有界变分映射中的关键作用，并指出超度量空间无需连续性即可满足该特征化。

Lagrangian stability for a system of non-local continuity equations under Osgood condition

We extend known existence and uniqueness results of weak measure solutions for systems of non-local continuity equations beyond the usual Lipschitz regularity. Existence of weak measure solutions holds for uniformly continuous vector fields and convolution kernels, while uniqueness follows from a Lagrangian stability estimate under an additional Osgood condition.