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math.AP2025
The Logarithmic Laplacian on General Graphs
Rui Chen, Wendi Xu
We establish, for the first time, a Bochner-type integral representation for the logarithmic Laplacian on weighted graphs. Assuming stochastic completeness of the underlying graph,…
math.AP2025
The Logarithmic Laplacian on Complete Riemannian Manifolds
Rui Chen
We introduce, for the first time, a Bochner representation of the logarithmic Laplacian on general complete Riemannian manifolds via spectral calculus and the heat semigroup. More…
math.AP2025
Existence and Convergence of Least-Energy Solutions Involving the Logarithmic Schrödinger Operator
Huyuan Chen, Rui Chen, Bobo Hua
In this paper, we study critical semilinear nonlocal elliptic equations involving the logarithmic Schrödinger operator and its fractional pseudo-relativistic counterpart, both aris…