4 papers
The boundary Harnack principle in a slit domain and its application to the Signorini problem
Chilin Zhang
We prove the regularity of the free boundary in the Signorini problem with variable coefficients. We use a boundary Harnack inequality in slit domain. The key…
Boundary regularity theory of the singular Lane-Emden-Fowler equation in a Lipschitz domain
Yahong Guo, Congming Li, Chilin Zhang
We study the singular Lane-Emden-Fowler equation \begin{equation} -Îu=f(X)\cdot u^{-γ} \end{equation} in a bounded Lipschitz domain , with the Dirichlet boundary condition an…
Optimal H{ö}lder convergence of a class of singular steady states to the Bahouri-Chemin patch
Yupei Huang, Chilin Zhang
Singular steady states are important objects in obtaining ill-posedness results for 2D incompressible Euler equations. In \cite{elgindi2022regular}, a family of singular steady sta…
A positive homogeneous fractional harmonic function in a Lipschitz cone
Chilin Zhang
We construct a positive function supported and solving in a Lipschitz cone. Such a function is unique up to a constant multiplication. Moreover, we show that it…