Calculus of variations on locally finite graphs

@article{Lin2021CalculusOV,
  title={Calculus of variations on locally finite graphs},
  author={Yong Lin and Yunyang Yang},
  journal={Revista Matem{\'a}tica Complutense},
  year={2021}
}
  • Yong Lin, Yunyang Yang
  • Published 2021
  • Mathematics
  • Revista Matemática Complutense
Let G = (V, E) be a locally finite graph. Firstly, using calculus of variations, including a direct method of variation and the mountain-pass theory, we get sequences of solutions to several local equations on G (the Schrödinger equation, the mean field equation, and the Yamabe equation). Secondly, we derive uniform estimates for those local solution sequences. Finally, we obtain global solutions by extracting convergent sequence of solutions. Our method can be described as a variational method… Expand
A heat flow for the mean field equation on a finite graph
  • Yong Lin, Yunyang Yang
  • Mathematics
  • Calculus of Variations and Partial Differential Equations
  • 2021
Inspired by works of Castéras (Pacific J. Math., 2015), Li-Zhu (Calc. Var., 2019) and Sun-Zhu (Calc. Var., 2020), we propose a heat flow for the mean field equation on a connected finite graph G =Expand

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