28 citations · 93 across the 27 of their papers we have counts for
27 papers
Instability of naked singularities of perfect fluid under gravitational perturbations
Junbin Li, Tingting Li, Xi-Ping Zhu
We study the instability of the naked singularities arising in the spherically symmetric self-similar collapsing of the Einstein--Euler system under gravitational perturbations. We…
Weyl's lemma on metric measure spaces
Yu Peng, Hui-Chun Zhang, Xi-Ping Zhu
In this paper, we extend the classical Weyl's lemma to metric measure spaces. As its applications, we show the local regularity of solutions for Poisson equations and a…
One-phase Free Boundary Problems on RCD Metric Measure Spaces
Chung-Kwong Chan, Hui-Chun Zhang, Xi-Ping Zhu
In this paper, we consider a vector-valued one-phase Bernoulli-type free boundary problem on a metric measure space with Riemannian curvature-dimension condition $RCD(K,N…
Quantitative gradient estimates for harmonic maps into singular spaces
Hui-Chun Zhang, Xiao Zhong, Xi-Ping Zhu
In this paper, we will show the Yau's gradient estimate for harmonic maps into a metric space with curvature bounded above by a constant , , in the sense of Al…
Weyl's law on metric measure spaces
Hui-Chun Zhang, Xi-Ping Zhu
In this paper, we will prove the Weyl's law for the asymptotic formula of Dirichlet eigenvalues on metric measure spaces with generalized Ricci curvature bounded from below.
Local Li-Yau's estimates on metric measure spaces
Hui-Chun Zhang, Xi-Ping Zhu
In this paper, we will study the (linear) geometric analysis on metric measure spaces. We will establish a local Li-Yau's estimate for weak solutions of the heat equation and prove…