6 citations · 8 across the 12 of their papers we have counts for
12 papers
Sharp Gagliardo-Nirenberg inequality and logarithmic Sobolev inequality on integer lattices
Yongjie Shi, Chengjie Yu
In this paper, we obtain a sharp Garliardo-Nirenberg inequality on integer lattices and characterize its rigidity. Moreover, as a consequence of the sharp Garliardo-Nirenberg inequ…
Extension and rigidity of Perrin's lower bound estimate for Steklov eigenvalues on graphs
Yongjie Shi, Chengjie Yu
In this paper, we extend a lower bound estimate for Steklov eigenvalues by Perrin \cite{Pe} on unit-weighted graphs to general weighted graphs and characterise its rigidity.
Comparisons of Dirichlet, Neumann and Laplacian eigenvalues on graphs and their applications
Yongjie Shi, Chengjie Yu
In this paper, we obtain some comparisons of the Dirichlet, Neumann and Laplacian eigenvalues on graphs. We also discuss their rigidities and some of their applications including s…
A Lichnerowicz-type estimate for Steklov eigenvalues on graphs and its rigidity
Yongjie Shi, Chengjie Yu
In this paper, we obtain a Lichnerowicz-type estimate for the first Steklov eigenvalues on graphs and discuss its rigidity.
Comparison of Steklov eigenvalues and Laplacian eigenvalues on graphs
Yongjie Shi, Chengjie Yu
In this paper, we obtain a comparison of Steklov eigenvalues and Laplacian eigenvalues on graphs and discuss its rigidity. As applications of the comparison of eigenvalues, we obta…
Uniqueness of exterior differentiation on locally finite graphs
Yongjie Shi, Chengjie Yu
In this short note, we prove the uniqueness of exterior differentiation on locally finite graphs.
Rigidity of a trace estimate for Steklov eigenvalues
Yongjie Shi, Chengjie Yu
In this short note, we show the rigidity of a trace estimate for Steklov eigenvalues with respect to functions in our previous work (Trace and inverse trace of Steklov eigenvalues.…
Higher order Dirichlet-to-Neumann maps on graphs and their eigenvalues
Yongjie Shi, Chengjie Yu
In this paper, we first introduce higher order Dirichlet-to-Neumann maps on graphs which can be viewed as a discrete analogue of the corresponding Dirichlet-to-Neumann maps on comp…
Critical points and surjectivity of smooth maps
Yongjie Shi, Chengjie Yu
Let be a smooth map between two differential manifolds with connected, closed and . In this short note, we show that either all the points of…
Smooth compositions with a nonsmooth inner function
Yongjie Shi, Chengjie Yu
In this paper, we present an interesting application of Baire's category theorem.
Trace and inverse trace of Steklov eigenvalues
Yongjie Shi, Chengjie Yu
In this paper, we obtain some new estimates for the trace and inverse trace of Steklov eigenvalues. The estimates generalize some previous results of Hersch-Payne-Schiffer , Brock}…
Trace and inverse trace of Steklov eigenvalues II
Yongjie Shi, Chengjie Yu
This is a continuation of our previous work arXiv:1601.05617 on trace and inverse trace of Steklov eigenvalues. More new inequalities for the trace and inverse trace of Steklov eig…