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math.AP2026
Supersolution Construction and Optimal Hardy Inequality for Fractional Laplacians
Philipp Hake, Matthias Keller, Felix Pogorzelski
We give a new criterion to show optimality of Hardy weights for general operators on graphs via the supersolution construction. For Laplacians on graphs without killing terms this…
math.AP2026
A Liouville Theorem for Domains in Graphs
Philipp Hake, Matthias Keller, Felix Pogorzelski +1
We show a Liouville theorem for domains in graphs with Dirichlet boundary conditions. More specifically, we characterize the non-existence of non-zero bounded harmonic functions. S…