20 citations · 110 across the 70 of their papers we have counts for
7 papers · 2 filters
An extension problem for the logarithmic Laplacian
Huyuan Chen, Daniel Hauer, Tobias Weth
The logarithmic Laplacian on the (whole) N-dimensional Euclidean space is defined as the first variation of the fractional Laplacian of order 2s at s=0 or, alternatively, as a sing…
Counting function and lower bound for Dirichlet eigenvalues of the m-order logarithmic Laplacian
Huyuan Chen, Long Chen
Our aim in this article is to obtain the limit of counting function for the Dirichlet eigenvalues involving the m-order logarithmic Laplacian in a bounded Lipschitz domain and to d…
Improved Lerey inequality and Trudinger-Moser type inequality involving the Leray potential
Huyuan Chen, Yihong Du, Feng Zhou
We obtain three types of results in this paper. Firstly we improve Leray's inequality by providing several types of reminder terms, secondly we introduce several Hilbert spaces bas…
The Cauchy problem associated to the logarithmic Laplacian with an application to the fundamental solution
Huyuan Chen, Laurent Véron
Let $\lnlap$ be the logarithmic Laplacian operator with Fourier symbol , we study the expression of the diffusion kernel which is associated to the equation $$\partial_tu…
On m-order logarithmic Laplacians and related propeties
Huyuan Chen
In this article, we study -order logarithmic Laplacian , which is a singular integro-differential operator with symbol by the Fourier t…
Liouville Theorem for semilinear elliptic inequalities with the fractional Hardy operators
Huyuan Chen, Ying Wang, Hichem Hajaiej
In this paper, we give a full classification of the nonexistence of positive weak solutions to the semilinear elliptic inequality involving the fractional Hardy potential in punctu…