8 papers · 1 filter
Optimal Stability Bounds, Minimizers, and Critical Points for a Critical Nonlocal Sobolev Inequality on the Heisenberg Group
Wenjing Chen, Zexi Wang
We investigate the optimal Bianchi-Egnell-type quantitative stability constant for the critical nonlocal Sobolev inequality on the Heisenberg group , \begin{equatio…
Remainder terms and sharp quantitative stability for a nonlocal Sobolev inequality on the Heisenberg group
Wenjing Chen, Zexi Wang
In this paper, we study the following nonlocal Sobolev inequality on the Heisenberg group \begin{equation}\label{eq:HLS} S_{HL}(Q,μ) \left(\int_{\mathbb{H}^{n}}\int_{\mathbb{H}^{n…
An extension of Cabré-Chanillo theorem to the -laplacian
Massimo Grossi, Luigi Montoro, Berardino Sciunzi +1
In this paper, we study the critical points of stable solutions for the following -laplacian equation \begin{equation*} \begin{cases} -div\big(|\nabla u|^{p-2}\nabla u\big)=f(u)…
Construction of solutions for the critical polyharmonic equation with competing potentials
Wenjing Chen, Zexi Wang
In this paper, we consider the following critical polyharmonic equation \begin{align*}%\label{abs} ( -Î)^m u+V(|y'|,y'')u=Q(|y'|,y'')u^{m^*-1},\quad u>0, \quad y=(y',y'')\in \math…
Blowing-up solutions for the Choquard type Brezis-Nirenberg problem in dimension three
Wenjing Chen, Zexi Wang
In this paper, we are interested in the existence of solutions for the following Choquard type Brezis-Nirenberg problem \begin{align*} \left\{ \begin{array}{ll} -Îu=\displaystyle\…
New type of solutions for a critical Grushin-type problem with competing potentials
Wenjing Chen, Zexi Wang
In this paper, we consider a critical Grushin-type problem with double potentials. By applying the reduction argument and local Pohouzaev identities, we construct a new family of s…