7 papers
Curvature estimate for the heteroclinical solution to a Bose-Einstein condensation system
Leyun Wu, Chilin Zhang
We investigate heteroclinical solutions of a vector-valued Bose-Einstein condensation system involving the -Laplacian. The main difficulty comes from the degeneracy of the -L…
Pointwise arbitrarily high-order interior estimates for mixed local and nonlocal elliptic equations
Pengyan Wang, Leyun Wu, Chilin Zhang
In this paper, we mainly focus on pointwise, arbitrarily high-order interior estimates for the mixed local-nonlocal elliptic equation \begin{equation*} (-Î)^{s}u(x)-Îu(x)=f(x),\q…
Liouville theorems for mixed local and nonlocal indefinite equations
Pengyan Wang, Leyun Wu
We investigate the qualitative properties of positive solutions to mixed local-nonlocal equations with indefinite nonlinearities, emphasizing the interaction between classical and…
On sliding methods for mixed local and nonlocal equations and Gibbons' conjecture
Yinbin Deng, Pengyan Wang, Zhihao Wang +1
We investigate elliptic and parabolic equations involving mixed local and nonlocal operators of the form , as well as their parabolic counterparts with both the Marchau…
Phase transitions in two-component Bose-Einstein condensates with Rabi frequency (I): The De Giorgi conjecture for the local problem in
Leyun Wu, Chilin Zhang
In this series of papers, we investigate coupled systems arising in the study of two-component Bose--Einstein condensates, and we establish classification results for solutions of…
Phase transitions in two-component Bose-Einstein condensates with Rabi frequency (II): The De Giorgi conjecture for the nonlocal problem in or
Leyun Wu, Chilin Zhang
In this series of papers, we investigate coupled systems arising in the study of two-component Bose-Einstein condensates, and we establish classification results for solutions of D…