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math.AP2024
A note for W^{1,p}(V) and W_0^{1,p}(V) on a locally finite graph
Yulu Tian, Liang Zhao
In this paper, we investigate the Sobolev spaces W^{1,p}(V) and W_0^{1,p}(V) on a locally finite graph G=(V,E), which are fundamental tools when we apply the variational methods to…
math.AP2024
Calculus of variations on hypergraphs
Mengqiu Shao, Yulu Tian, Liang Zhao
We have established a coherent framework for applying variational methods to partial differential equations on hypergraphs, which includes the propositions of calculus and function…
math.AP2022
Normalized solution to the nonlinear p-Laplacian equation with an L^2 constrain: mass supercritical case
Yulu Tian, Deng-Shan Wang, Liang Zhao
In this paper, we study the existence of ground state solutions to the following p-Laplacian equation in some dimension with an constraint: \begin{equation*} \begin{…