7 citations · 47 across the 26 of their papers we have counts for
26 papers
Blow up analysis for Keller-Segel system
Hua Chen, Jian-Meng Li, Kelei Wang
In this paper we develop a blow up theory for the parabolic-elliptic Keller-Segel system, which can be viewed as a parabolic counterpart to the Liouville equation. This theory is a…
Nondegeneracy for stable solutions to the one-phase free boundary problem
Nikola Kamburov, Kelei Wang
We prove the nondegeneracy condition for stable solutions to the one-phase free boundary problem. The proof is by a De Giorgi iteration, where we need the Sobolev inequality of Mic…
Refined blowup analysis and nonexistence of Type II blowups for an energy critical nonlinear heat equation
Kelei Wang, Juncheng Wei
We consider the energy critical semilinear heat equation $$ \left\{\begin{aligned} &\partial_t u-Δu =|u|^{\frac{4}{n-2}}u &\mbox{in } {\mathbb R}^n\times(0,T),\\ &u(x,0)=u_0(x), \e…
Lipschitz property of bistable or combustion fronts and its applications
Kelei Wang
For a class of reaction-diffusion equations describing propagation phenomena, we prove that for any entire solution , the level set is a Lipschitz graph in the time di…
A generalized one phase Stefan problem as a vanishing viscosity limit
Kelei Wang
We study the vanishing viscosity limit of a nonlinear diffusion equation describing chemical reaction interface or the spatial segregation interface of competing species, where the…
Stability of the saddle solutions for the Allen-Cahn equation
Yong Liu, Kelei Wang, Juncheng Wei
We are concerned with the saddle solutions of the Allen-Cahn equation constructed by Cabré and Terra \cite{C,C2} in . These so…
Axially symmetric solutions of Allen-Cahn equation with finite Morse index
Changfeng Gui, Kelei Wang, Juncheng Wei
In this paper we study axially symmetric solutions of Allen-Cahn equation with finite Morse index. It is shown that there does not exist such a solution in dimensions between a…
Half space theorem for the Allen-Cahn equation and related problems
Francois Hamel, Yong Liu, Pieralberto Sicbaldi +2
In this paper we obtain rigidity results for a bounded non-constant entire solution of the Allen-Cahn equation in , whose level set is contained in a ha…
Second order estimates on transition layers
Kelei Wang, Juncheng Wei
In this paper we establish a uniform estimate for level sets of stable solutions to the singularly perturbed Allen-Cahn equation in dimensions (which is optim…
On one phase free boundary problem in
Yong Liu, Kelei Wang, Juncheng Wei
We construct a smooth axially symmetric solution to the classical one phase free boundary problem in . Its free boundary is of \textquotedblleft catenoid\textquoted…
Finite Morse index implies finite ends
Kelei Wang, Juncheng Wei
We prove that finite Morse index solutions to the Allen-Cahn equation in have {\bf finitely many ends} and {\bf linear energy growth}. The main tool is a {\bf curvature deca…
On a free boundary problem and minimal surfaces
Yong Liu, Kelei Wang, Juncheng Wei
From minimal surfaces such as Simons' cone and catenoids, using refined Lyapunov-Schmidt reduction method, we construct new solutions for a free boundary problem whose free boundar…
Asymptotics for the fractional Allen-Cahn equation and stationary nonlocal minimal surfaces
Vincent Millot, Yannick Sire, Kelei Wang
This article is mainly devoted to the asymptotic analysis of a fractional version of the (elliptic) Allen-Cahn equation in a bounded domain , with or without…
Global minimizers of the Allen-Cahn equation in dimension
Yong Liu, Kelei Wang, Juncheng Wei
We prove the existence of global minimizers of Allen-Cahn equation in dimensions and above. More precisely, given any strictly area-minimizing Lawson's cones, there are global…
Uniform Lipschitz regularity of flat segregated interfaces in a singularly perturbed problem
Kelei Wang
For the singularly perturbed system \[Δu_{i,β}=βu_{i,β}\sum_{j\neq i}u_{j,β}^2, \quad 1\leq i\leq N,\] we prove that flat interfaces are uniformly Lipschitz. As a byproduct of the…
Some remarks on the structure of finite Morse index solutions to the Allen-Cahn equation in
Kelei Wang
For a solution of the Allen-Cahn equation in , under the natural linear growth energy bound, we show that the blowing down limit is unique. Furthermore, if the soluti…
The structure of finite Morse index solutions to two free boundary problems in
Kelei Wang
We give a description of the structure of finite Morse index solutions to two free boundary problems in . These free boundary problems are models of phase transition…
On Serrin's overdetermined problem and a conjecture of Berestycki, Caffarelli and Nirenberg
Kelei Wang, Juncheng Wei
This paper concerns rigidity results to Serrin's overdetermined problem in an epigraph $$ \{\begin{aligned} &Δu+ f(u)=0,\ \ \ {in}\ Ω=\{(x^\prime,x_n): x_n>φ(x^\prime)\},\\ &u>0,\…
On the uniqueness of solutions of an nonlocal elliptic system
Kelei Wang, Juncheng Wei
We consider the following elliptic system with fractional laplacian $$ -(-Δ)^su=uv^2,\ \ -(-Δ)^sv=vu^2,\ \ u,v>0 \ \mbox{on}\ \R^n,$$ where and is the -Lapa…
Harmonic approximation and improvement of flatness in a singular perturbation problem
Kelei Wang
We study the De Giorgi type conjecture, that is, one dimensional symmetry problem for entire solutions of an two components elliptic system in , for all . We…
A new proof of Savin's theorem on Allen-Cahn equations
Kelei Wang
In this paper we establish an improvement of tilt-excess decay estimate for the Allen-Cahn equation, and use this to give a new proof of Savin's theorem on the uniform re…
Qualitative Analysis of Rupture Solutions for an MEMS Problem
Juan Davila, Kelei Wang, Juncheng Wei
We prove a sharp Hölder continuity estimates of rupture sets for sequences of solutions of the following nonlinear problem with negative exponent $$ Δu= \frac{1}{u^p}, \ p>1, \ \mb…
A Monotonicity Formula and a Liouville-type Theorem for a Fourth Order Supercritical Problem
Juan Davila, Louis Dupaigne, Kelei Wang +1
We consider Liouville-type and partial regularity results for the nonlinear fourth-order problem $$ Δ^2 u=|u|^{p-1}u\ \{in} \ \R^n,$$ where and . We give a complete c…
On solutions with polynomial growth to an autonomous nonlinear elliptic problem
Kelei Wang, Juncheng Wei
We study the following nonlinear elliptic problem [-Δu =F^{'} (u) in {\mathbb R}^n] where is a periodic function. Moser (1986) showed that for any minimal and nonself-inters…