5 citations · 9 across the 5 of their papers we have counts for
6 papers
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…
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…
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 $$ \{\begin{aligned} &Δu+ f(u)=0,\ \ \ {in}\ Ω=\{(x^\prime,x_n): x_n>φ(x^\prime)\},\\ &u>0,\…
Qualitative Analysis of Rupture Solutions for an MEMS Problem
Juan Davila, Kelei Wang, Juncheng Wei
We prove a sharp Hölder continuity estimates of rupture sets for sequences of solutions of the following nonlinear problem with negative exponent $$ 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…