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Fractional Sobolev spaces and fractional -Laplace equations on locally finite graphs
Mengjie Zhang, Yong Lin, Yunyan Yang
Graph-based analysis holds both theoretical and applied significance, attracting considerable attention from researchers and yielding abundant results in recent years. However, res…
Fractional Laplace operator and related Schrödinger equations on locally finite graphs
Mengjie Zhang, Yong Lin, Yunyan Yang
In this paper, we first define a discrete version of the fractional Laplace operator through the heat semigroup on a stochastically complete, connected, locally finite g…
Fractional Laplace operator on finite graphs
Mengjie Zhang, Yong Lin, Yunyan Yang
Nowadays a great attention has been focused on the discrete fractional Laplace operator as the natural counterpart of the continuous one. In this paper, we discretize the fractiona…
Topological degree for Chern-Simons Higgs models on finite graphs
Jiayu Li, Linlin Sun, Yunyan Yang
Let be a finite connected graph. We are concerned about the Chern-Simons Higgs model where is the graph Lapl…
Trudinger-Moser inequalities on a closed Riemann surface with a symmetric conical metric
Yu Fang, Yunyan Yang
This is a continuation of our previous work [13]. Let be a closed Riemann surface, where the metric has conical singularities at finite points. Suppose is…