| Abstract: |
| This talk considers the $p$-biharmonic equation on graphs, which arises in point cloud processing and can be interpreted as a natural extension of the graph $p$-Laplacian from the perspective of hypergraphs. The asymptotic behavior of the solution is discussed for the random geometric graph when the number of data points goes to infinity. We show that the continuum limit is an appropriately weighted $p$-biharmonic equation with homogeneous Neumann boundary conditions. The result relies on the uniform $L^p$ estimates for solutions and gradients of nonlocal and graph Poisson equations. |
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