7 papers
Global Convergence of the Gursky-Malchiodi -curvature Flow
Liuwei Gong, Sanghoon Lee, Juncheng Wei
In their seminal work, Gursky and Malchiodi introduced a non-local conformal flow in dimensions to resolve the constant -curvature problem. They proved sequential con…
The Rabinowitz continuum of subcritical Gelfand problems and free boundary-type equations arising in plasma physics
Daniele Bartolucci, Aleks Jevnikar, Juncheng Wei +1
The qualitative behavior of the Rabinowitz unbounded continuum of subcritical Gelfand problems is well known on balls in any dimension. We don't know of any such sharp and detailed…
A Lane-Emden system of free boundary type: existence, uniqueness and monotonicity of solutions
Daniele Bartolucci, Yeyao Hu, Aleks Jevnikar +2
We consider a Hamiltonian system of free boundary type, showing first uniform bounds and existence of solutions and of the free boundary. Then, for any smooth and bounded domain, w…
Classification of singular limits for free boundary and singularly perturbed elliptic problems: the Dancer-Yan spikes revisited
Daniele Bartolucci, Aleks Jevnikar, Juncheng Wei +1
We classify the singular limits relative to a free boundary problem arising in plasma physics in dimension , under suitable natural integral bounds. It turns out that one of t…
Symmetry in Serrin-type overdetermined problems
Daomin Cao, Juncheng Wei, Weicheng Zhan
This paper investigates the geometric constraints imposed on a domain by overdetermined problems for partial differential equations. Serrin's symmetry results are extended to overd…
Localized patterns in the Gierer Meinhardt model on a cycle graph
Theodore Kolokolnikov, Juncheng Wei, Shuangquan Xie
In this study, we provide a detailed analysis of the spike solutions and their stability for theGierer-Meinhardt model on discrete lattices. We explore several phenomena that have…
An Ohta-Kawasaki Model set on the space
Lorena Aguirre Salazar, Xin Yang Lu, Jun-cheng Wei
We examine a non-local diffuse interface energy with Coulomb repulsion in three dimensions inspired by the Thomas-Fermi-Dirac-von Weizsäcker, and the Ohta-Kawasaki models. We consi…